Question

what is the inverse of f(x)=(-2x+2)/(x+7)?

Answer 1

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

How to find the inverse of a function

In this question we have a rational function f(x) and finding its inverse consists in clearing x in terms of f(x). Prior any algebraic handling, we need to apply the following substitutions:

$x \to y$

$f(x) \to x$

$x = \frac{-2\cdot y + 2}{y+7}$

x · (y + 7) = - 2 · y + 2

x · y + 7 · x = - 2 · y + 2

2 · y + x · y = - 7 · x + 2

y · (2 + x) = - 7 · x + 2

$g(x) = \frac{- 7\cdot x + 2}{x + 2}$

By applying the concept of the inverse of a function and algebraic handling, we conclude that the inverse of f(x) = (- 2 · x + 2)/(x + 7) is g(x) = (- 7 · x + 2)/(x + 2).

To learn more on inverses: https://brainly.com/question/7181576

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