Inverse Functions Calculator

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Example

Created on 2024-06-20Asked by Scarlett Thomas (Solvelet student)

Find the inverse function of

f(x) = \frac{2x + 3}{x - 1}

Solution

To find the inverse function of

f(x) = \frac{2x + 3}{x - 1}

, follow these steps: 1. Replace

f(x)

with

y

y = \frac{2x + 3}{x - 1}

2. Solve for

x

in terms of

y

y(x - 1) = 2x + 3

yx - y = 2x + 3

yx - 2x = y + 3

x(y - 2) = y + 3

x = \frac{y + 3}{y - 2}

3. Replace

y

with

x

to get the inverse function:

f^{-1}(x) = \frac{x + 3}{x - 2}

Therefore, the inverse function of

f(x) = \frac{2x + 3}{x - 1}

is:

f^{-1}(x) = \frac{x + 3}{x - 2}

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Sofia Nelson on Solvelet

1. Find the inverse function of

f(x) = 2x + 3

,2. Find the time-domain solution

f(t)

given its Laplace transform

F(s) = \frac{s + 2}{s^2 + 2s + 1}

DefinitionFrom an inverse perspective, it take the result and the function to return back to the original input. If a function f(x) has a inverse function f−1(y) then f(f−1(y))=y and f−1(f(x)) = x. Inverse functions are used for solving equations, modeling, and for understanding the relation of variables. We achieve them by solving y=f(x) in regard to y for x, example: f(x)=2x+3 then f−1(y)=2y−3. Hence If f(x)=y then f−1(y)=x, such that f(f−1(y))=y and f−1(f(x))=x.

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