What Are Inverse Functions?
Read this topicExplanations 4
- In a function, each input has one output. For any one-to-one function (only one value of yyy for every xxx), the inverse function "undoes" the original function. Another way to …
By Daniel Hu, Benjamin Qi
- Inverses of Compositions In this explanation I'm going to talk about how to find the inverse of a composition of functions. Before going on you may want to read about simplifyin…
By Joshua Siktar, Victor Wang, Gabi Slizewska, Anusha Rahman
- Inverse Functions Inverse functions are functions where the xxx and yyy coordinates are flipped. That is essentially a reflection over the line y=xy=xy=x. A function must be one…
By Anusha Rahman
- (Video) Inverse Functions by Professor Dave Explains In this video, Professor Dave Explains walks you through what an inverse function is. Summary We know that when we put a val…
By Anusha Rahman
Problems 42
- Assuming fff is invertible, what is f(f−1(3))f(f^{-1}(3))f(f−1(3))?
- Let fff be an invertible function (i.e. a function which passes the horizontal line test) and ggg be any function. In terms of fff and ggg, find a function hhh which satisfies f…
- Let f(x)=x+3f(x) = \sqrt{x}+3f(x)=x+3 for all x≥0x \ge 0x≥0. What is the domain of f−1f^{-1}f−1 (where f−1f^{-1}f−1 is the function which satisfies f(f−1(x))=xf(f^{-1}(x)) = xf…
- Assume this function is one-to-one If f(6)=7f(6)=7f(6)=7, find f−1(7)f^{-1}(7)f−1(7)
- Assume this function is one-to-one If f(3)=2f(3)=2f(3)=2, find f−1(2)f^{-1}(2)f−1(2)
- Assume this function is one-to-one If f−1(−4)=−8f^{-1}(-4)=-8f−1(−4)=−8, find f(−8)f(-8)f(−8)
- Assume this function is one-to-one If f−1(−2)=−1f^{-1}(-2)=-1f−1(−2)=−1, find f(−1)f(-1)f(−1)
- Assume this function is one-to-one If f(5)=2f(5)=2f(5)=2, find (f(5))−1(f(5))^{-1}(f(5))−1
- Assume this function is one-to-one If f(1)=4f(1)=4f(1)=4, find (f(1))−1(f(1))^{-1}(f(1))−1
- Using the graph of f(x)f(x)f(x) shown, which are correct?
- Using the graph of f(x)f(x)f(x) shown, which are correct?
- Using the table above, which are correct?
- Using the table above, which are correct?
- For f(x)=x+3f(x)=x+3f(x)=x+3, what is f−1(x)f^{-1}(x)f−1(x)?
- For f(x)=x+5f(x)=x+5f(x)=x+5, what is f−1(x)f^{-1}(x)f−1(x)?
- For f(x)=2−xf(x)=2-xf(x)=2−x, what is f−1(x)f^{-1}(x)f−1(x)?
- For f(x)=3−xf(x)=3-xf(x)=3−x, what is f−1(x)f^{-1}(x)f−1(x)?
- For f(x)=11x+7f(x)=11x+7f(x)=11x+7, what is f−1(x)f^{-1}(x)f−1(x)?
- For f(x)=9+10xf(x)=9+10xf(x)=9+10x, what is f−1(x)f^{-1}(x)f−1(x)?
- For f(x)=(x+7)2f(x)=(x+7)^2f(x)=(x+7)2 find a domain on which fff is one-to-one and non-decreasing, then find the inverse of fff restricted to that domain.
- For f(x)=x2−5f(x)=x^2-5f(x)=x2−5, find a domain on which fff is one-to-one and non-decreasing, then find the inverse of fff restricted to that domain.
- f(x)=x3−5f(x)=x^3-5f(x)=x3−5 and g(x)=x+53g(x)=\sqrt[3]{x+5}g(x)=3x+5, find a. f(g(x))f(g(x))f(g(x)) b. g(f(x))g(f(x))g(f(x))
- f(x)=x2+x f(x)=\dfrac x{2+x}\:f(x)=2+xx and g(x)=2x1−x g(x)=\dfrac{2x}{1-x}\:g(x)=1−x2x, find a. f(g(x))f(g(x))f(g(x)) b. g(f(x))g(f(x))g(f(x))
- Function fff is defined only on the domain of integers [0,6][0, 6][0,6], fff has an inverse, and f(2)f(2)f(2) = a number nnn. What is f−1(n)f^{-1}(n)f−1(n)?
- Function fff is defined only on the domain of integers [0,6][0, 6][0,6], fff has an inverse, and f(2)=3f(2) = 3f(2)=3. Also, f(6)=4f(6) = 4f(6)=4. What is f−1(4)f^{-1}(4)f−1(4)?
- If f(x)=3x+8f(x)= 3x+8f(x)=3x+8, find the inverse function.
- If f(x)=x2+x+1xf(x)= \dfrac{x^2+x+1}{x}f(x)=xx2+x+1, find f−1(x)f^{-1}(x)f−1(x).
- Find the inverse of f(x)=2x−63x+7f(x)=\dfrac{2x-6}{3x+7}f(x)=3x+72x−6
- Find the inverse of f(x)=x3−7f(x)= x^3-7f(x)=x3−7
- Find the inverse of f(x)=7x3−16f(x) = \dfrac{7x}{3} -\dfrac{1}{6}f(x)=37x−61
- If f(x)=(x−2)3f(x)= (x-2)^3f(x)=(x−2)3, find the inverse.
- If f(x)=2x−73f(x)= \dfrac{2x-7}{3}f(x)=32x−7, find f−1(x)f^{-1}(x)f−1(x).
- If f(x)=ln(x−5)f(x)= \ln(x-5)f(x)=ln(x−5), find the inverse function.
- Find the inverse of the function f(x)=1x2f(x)=\dfrac {1}{x^2}f(x)=x21
- If f(x)=−3x+11f(x)= -3x+11f(x)=−3x+11, find the inverse of the function.
- Find the inverse of the function: f(x)=x−5f(x)= \sqrt{x-5}f(x)=x−5
- Find the inverse of the function: f(x)=32x+152f(x) = \dfrac{3}{2} x + \dfrac{15}{2}f(x)=23x+215
- Find the inverse of the function: f(x)=6+xf(x) = 6+ \sqrt {x}f(x)=6+x
- Find the inverse of f(x)=(x−3)7f(x)= (x-3)^7f(x)=(x−3)7
- Assume the function fff is one-to-one. \\ If f(13)=8f(13) = 8f(13)=8, find f−1(8)f^{-1} (8)f−1(8).
- If f(x)=log9(x3+17)f(x)= \log_{9}(x^3+17)f(x)=log9(x3+17), find the inverse of f(x)f(x)f(x).
- Find the inverse of the function: f(x)=e1xf(x) = e^{\frac{1}{x}}f(x)=ex1.