• Tweet This • Bookmark on Delicious • Share on FacebookPrecalculus We find the domain and range of the function f(x) = 1/(x^22x8) Two approaches are used the first uses the graph of the parabola y=x^2x8, Misc 5 Find the domain and the range of the real function f defined by f (x) = x – 1 Here we are given a real function Hence, both domain and range should be real numbers Here, x can be any real number Here, f (x) will always be positive or zero Here value of domain (x) can be any real number Hence, Domain = R (All real numbers) We note that that range f (x) is 0 or positive numbers, So range cannot be negative Hence, Range
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F(x)=1/1-x^2 find domain and range-Algebra Find the Domain and Range F (x)=1/ (x^2) F (x) = 1 x2 F ( x) = 1 x 2 Set the denominator in 1 x2 1 x 2 equal to 0 0 to find where the expression is undefined x2 = 0 x 2 = 0 Solve for x x Tap for more steps Take the square root of both sides of the equation to eliminate the exponent on the left side x = ± √ 0 x = ± 0How to Find the Domain and Range of f(x, y) = ln(xy 2)If you enjoyed this video please consider liking, sharing, and subscribingYou can also help support
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Enter your queries using plain English To avoid ambiguous queries, make sure to use parentheses where necessary Here are some examples illustrating how to ask for the domain and range domain of log(x) (x^21)/(x^21) domain; Find the range of function f(x) = cot^1(2x x^2) asked in Sets, relations and functions by SumanMandal ( 546k points) inverse trigonometric functionsWhat is the domain and range of f(x)=1/sqrt (9x^2)?
Domain of f (x) is − ∞, ∞) From ( 1 ), The range of f (x) = 3 x 2 7 x 1 0 is Medium View solution > If the range of the function f (x) = 6To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Find domain and range of `f(x)=x/(1x^2)` Find the domain and range of a function f(x)=1/(1x^2) Forums Maths, Math, Homework, Do My Homework Email this Topic • Print this Page Swapnil Reply Mon 23 Jun, 14 1144 am Find the domain and range of a function f(x)=1/(1x^2) Stumble It!
For instance, f (x) = The domain is simply the denominator set equal to 0, {xl x≠3} However, range is found by solving for (isolating x to one side) and setting the denominator equal to zero x = So range is {xl x≠0} This is a systematic method that I assume is the only way to find the range 2x 1 = 0 2x = 1 x = 1 / 2 Therefore , Domain = R { 1/2 } All real numbers are used as range here For getting solve the denominator of the given fraction and reduce the value of x from the real number "R" Hope it helps you dude Given f(x) = 1x2 To find the range of function Explanation So, the range of a function consists of all the second elements of all the ordered pairs, ie, f(x), so we have to find the values of f(x) to get the required range Given, f(x) = 1x2 Now for real value of f, x2≥ 0 Adding negative sign, we get Or x2≤ 0 Adding
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The domain of the function will thus be ( −∞, − 1) ∪(1, ∞) The range of the function will be determine by the fact that the square root will always give a positive value for real numbers This means that the range of the will be 0, ∞) graph {sqrt (x^21) 79, 7904, 3946, 3956} Answer linkFind the domain of 1/(e^(1/x)1) function domain square root of cos(x) log(1x^2) domain; Step 1 Draw the graph Step 2 Find the possible values of x where f (x) is defined Here the x values start from 2 and ends in 2 Step 3 The possible values of x is the domain of the function ∴ \therefore ∴ the domain of the circle is { x ϵ R − 2 ≤ x ≤ 2 x\epsilon \mathbb {R}2\leq x\leq 2 xϵR −2 ≤ x ≤ 2 } =
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What is the domain and range of the real function f(x)=1/(1x^2)?For domain under root should not be n egative quantity, 16−x2 ≥ 0 16≥ x2 Therefore, x ≤ 4 or x ≥ −4 Then, The domain−4,4 Range f (x) is maximum at x= 0,f (x)= 4 And f (x) is minimum at x= 4,f (xX, y ∈ R Let y = f (x) Then y = 1 1 − x 2 y = 1 (1 x) (1 − x) means that x ≠ ± 1 because the denominator cannot be 0 So the domain of f is {x x ≠ − 1 or x ≠ 1} To find the range, get x in terms of y y = 1 1 − x 2 y (1 − x 2) = 1 y − x 2 y = 1 − x 2 y = 1 − y x 2 y = y − 1
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Arithmetic Mean Geometric Mean Quadratic Mean Median Mode Order Minimum Maximum Probability MidRange Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution f(x)=\frac{1}{x^2} domain\y=\frac{x}{x^26x8} domain\f(x)=\sqrt{x3} domain\f(x)=\cos(2x5) domain\f(xClearly, f(x) is defined for all x ∈ R except for which x2 − 1 = 0 ie, x = ± 1 Hence, Domain of f = R − { − 1, 1} Let f(x) = y Then, 1 1 − x2 = y ⇒ 1 − x2 = 1 y ⇒ x2 = 1 − 1 y = y − 1 y ⇒ x = ± √y − 1 y − 0 Clearly, x will take real values, ifThe domain is easy to find The denominator must be nonzero, and the quantity being squarerooted must be nonnegative Combine these two conditions The range could cause us some trouble To begin with, note that the function is always positive, as per the definition of the square root
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Find the domain and range of the function `f(x)=(1)/sqrt(x5)`For the reciprocal squared function latexf\left(x\right)=\frac{1}{{x}^{2}}/latex, we cannot divide by latex0/latex, so we must exclude latex0/latex from the domain There is also no latexx/latex that can give an output of 0, so 0 is excluded from the range as well Note that the output of this function is always positive due to the square in the denominator, so the range To find The domain and range of the real function Solution To find domain Equate the denominator to zero Denominator (3x)=0 x=3 This means at x=3 function is not defined And by definition of domain The domain is where the function is not defined Domain is Range Put f(x)=y Range is the set of value that correspond to domain
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Range of arccot(x) View more examples » Find the domain and range of the following real functions f(x)=x^29/x3 asked Feb 9 in Sets, Relations and Functions by Ekaa ( 268k points) relations and functions 1 Confirm that you have a quadratic function A quadratic function has the form ax 2 bx c f (x) = 2x 2 3x 4 The shape of a quadratic function on a graph is parabola pointing up or down There are different methods to calculating the range of a function depending on the type you are working with
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Example 1 Find the domain and range of the following functions f(x) = 1/(2 sin 3x) Solution In order to find the domain, let us equate the denominator to 0 2 sin 3x = 0 sin 3x = 2 This is impossible, because the minimum value of sin is 1 and maximum value is 1Example 1 Find the domain and range of the function y = 3 x 2 Graph the function on a coordinate plane The graph is nothing but the graph y = 3 x translated 2 units to the left The function is defined for all real numbers So, the domain of the function is set of real numbersTo find the domain, let f(x)=1/log(2x) is not defined for 1 2x
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To answer this problem, the first thing we can consider is if there are any values, for what the function, f(x) is undifined at, this would be where the denominator =0 => 1 e^(2x) = 0 => e^(2x) = 1 => 2x = ln(1) => x = 1/2 ln(1) We know 1/2 ln(1) notin RR So hence the denominator is defined AAx in RR ( defined for all x values in the real set) We also know e^(2x) is also defined AAx in RR So hence f(x) is defined for AAx in RR Domain x in RR (for all real values of x )F(x)=1/(4x^21) The domain is x values in which the function is defined Since the function is a root, then the denominator (4x^21) should not be zeroFind the Domain and Range f (x)=x^2 f (x) = x2 f ( x) = x 2 The domain of the expression is all real numbers except where the expression is undefined In this case, there is no real number that makes the expression undefined Interval Notation (−∞,∞) ( ∞, ∞) Set Builder Notation {xx ∈ R} { x x
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Domain of f ( x) = sin ( ln ( 1 − x 4 − x 2 )) is Medium View solution > The value of x for which the function 2 x − 5 1 is not defined Medium View solution > A = the domain of f where f ( x) = lo g x 2 and B = the domain of g where g ( x) = 2 lo g x, then A − B =This is a revised answer!What are the domain and range of the realvalued function f(x) = −3x 2 6x 1?
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The function f(x) = x 2 has a domain of all real numbers (x can be anything) and a range that is greater than or equal to zero Two ways in which the domain and range of a function can be written are interval notation and set notationAlgebra Find the Domain and Range f (x)=1/x f (x) = 1 x f ( x) = 1 x Set the denominator in 1 x 1 x equal to 0 0 to find where the expression is undefined x = 0 x = 0 The domain is all values of x x that make the expression defined Interval Notation Find the domain and range of the real function f (x) = x/1x^2 ━━━━━━━━━━━━━━━━━━━━━━━━━ ️Given real function is f (x) = x/1x^2 ️1 x^2 ≠ 0 ️x^2 ≠ 1 ️Domain x ∈ R
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Algebra Find the Domain and Range f (x)=x^21 f (x) = x2 1 f ( x) = x 2 1 The domain of the expression is all real numbers except where the expression is undefined In this case, there is no real number that makes the expression undefined Interval NotationIf x denotes the integral part of x, then domain of the function f (x) = g (x) h (x), where g (x) = (x − 1) (x − 2) (x − 3) 3 − x and h (x) = sin − 1 2 3 x − 2 is 0, 2) − {1} ReasonFind the domain and range of the function f (x) = 2 − sin3x1 Solution Solution f (x) = 2 − sin3x1 Here, 2 − sin3x can never be zero as sin3x will always less than 2 ∴ Domain of f (x) will be x ∈ R Now, f (x) will be maximum when 2 − sin3x is minimum 2 − sin3x will be minimum when sin3x = 1
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Find the domain of each of the following functions given by f(x) = (x^3 x 3)/(x^2 1) asked in Sets, Relations and Functions by RamanKumar (This is a quadratic function There are no rational or radical expressions, so there is nothing that will restrict the domain Any real number can be used for x to get a meaningful output Because the coefficient of x 2 is negative, it will open downward WithSo, the range is 0, ∞) Question 2 Find the domain and range of the following functions f(x) = 1 x 2 Solution For any values values of x, the function will give defined values It will never become undefined So, domain is all real values that is R The range of x 2 lies between 0 to ∞ But we need find the range of 1 x
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The given real function is f (x) = x − 1 It can be seen that x − 1 is defined for (x − 1) ≥ 0 ie, f (x) = (x − 1) is defined for x ≥ 1 Therefore the domain of f is the set of all real numbers greater than or equal to 1 ie, the domain of f = 1, ∞)Calculus Find the Domain and Range f (x)= (x1)/ (x1) f (x) = x − 1 x 1 f ( x) = x 1 x 1 Set the denominator in x−1 x1 x 1 x 1 equal to 0 0 to find where the expression is undefined x1 = 0 x 1 = 0 Subtract 1 1 from both sides of the equation x = −1 x = 1 Misc 4 Find the domain and the range of the real function f defined by f(x) = √((𝑥−1)) It is given that the function is a real function Hence, both its domain and range should be real numbers x can be a number greater 1 Here, f(x) is always positive, Minimum value of f(x) is 0,
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