Find the inverse of f(x)= 2x+3/x-1

Question

asked Sep 4, 2021 88.2k views

1 Answer

Manzapanza · Answer 1 · 2021-09-11T07:31:45+0000

Answer:

$\displaystyle f^(-1)(x)=(3+x)/(x-2)$

Explanation:

We have the function:

$\displaystyle f(x)=(2x+3)/(x-1)$

Find the inverse of f(x). First, we call y=f(x):

$\displaystyle y=(2x+3)/(x-1)$

We have to solve for x. Multiply by x-1:

y(x-1)=2x+3

Operate:

yx-y=2x+3

Join all the x's to the left side and move the rest to the right side:

yx-2x=3+y

Factor:

x(y-2)=3+y

Solve for x:

$\displaystyle x=(3+y)/(y-2)$

Interchange the variables:

$\displaystyle y=(3+x)/(x-2)$

This is the inverse function:

$\boxed{\displaystyle f^(-1)(x)=(3+x)/(x-2)}$