Inverse function practice problems with answers pdf

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Section 3-7 : Inverse Functions
How do you solve inverse function questions?
How do you solve an inverse step by step?
What are inverse function examples?
How do you calculate inverse?

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Section 3-7 : Inverse Functions

Given \(h\left( x \right) = 5 - 9x\) find \({h^{ - 1}}\left( x \right)\). Solution
Given \(\displaystyle g\left( x \right) = \frac{1}{2}x + 7\) find \({g^{ - 1}}\left( x \right)\). Solution
Given \(f\left( x \right) = {\left( {x - 2} \right)^3} + 1\) find \({f^{ - 1}}\left( x \right)\). Solution
Given \(A\left( x \right) = \sqrt[5]{{2x + 11}}\) find \({A^{ - 1}}\left( x \right)\). Solution
Given \(\displaystyle f\left( x \right) = \frac{{4x}}{{5 - x}}\) find \({f^{ - 1}}\left( x \right)\). Solution
Given \(\displaystyle h\left( x \right) = \frac{{1 + 2x}}{{7 + x}}\) find \({h^{ - 1}}\left( x \right)\). Solution

How do you solve inverse function questions?

How to find inverse functions.

Write out the expression for the original function using a y instead of the x. Set this expression equal to. x. x..

Rearrange the equation to make y the subject..

Write your inverse function using the f − 1 f^{-1} f−1 notation..

How do you solve an inverse step by step?

Steps for finding the inverse of a function f..

Replace f(x) by y in the equation describing the function..

Interchange x and y. In other words, replace every x by a y and vice versa..

Solve for y..

Replace y by f-1(x)..

What are inverse function examples?

The inverse function returns the original value for which a function gave the output. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value. Then, g(y) = (y-5)/2 = x is the inverse of f(x).

How do you calculate inverse?

How do you find the inverse of a function? To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.