39.2k views
4 votes
Find the inverse function of f(x) = x+2/x+1

User Hannele
by
9.1k points

2 Answers

3 votes

Answer:


f^(-1)(x) =
(2-x)/(x-1)

Explanation:

Let y = f(x) and rearrange making x the subject

y =
(x+2)/(x+1) ( multiply both sides by (x + 1)

y(x + 1) = x + 2 ← distribute left side

yx + y = x + 2 ( subtract x from both sides )

yx - x + y = 2 ( subtract y from both sides )

yx - x = 2 - y ← factor out x on the left side

x(y - 1) = 2 - y ← divide both sides by (y - 1 )

x =
(2-y)/(y-1)

Change y back into terms of x, thus


f^(-1)(x) =
(2-x)/(x-1)

User Zeograd
by
8.4k points
4 votes

Answer:
\bold{f^(-1)(x)=(2-x)/(x-1)\qquad \implies \qquad f^(-1)(x)=-(x-2)/(x-1)}

Explanation:

Inverse is when you swap the x's and y's and solve for y. f(x) is y.


y=(x+2)/(x+1)\\\\\\\\\underline{\text{Swap the x's and y's}}\\\\x=(y+2)/(y+1)\\\\\\\\\underline{\text{solve for y}}\\\\x(y+1)=y+2\\\\xy+x=y+2\qquad \qquad \text{distributed x into y+1}\\\\xy-y=2-x\qquad \qquad \text{subtracted x and y from both sides}\\\\y(x-1)=2-x\qquad \qquad \text{factored out y on the left side}\\\\\\y=(2-x)/(x-1)}\qquad \qquad \text{divided both sides by x-1}


\large\boxed{f^(-1)(x)=(2-x)/(x-1)}

This is equal to:
f^(-1)(x)=-(x-2)/(x-1)

User Bjhuffine
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories