Please help

Question

I don't remember how to do these types of problems, please help

 

Find f−1(x) for the following function:

f(x)=(3)/(x−5)−2

Answer 1

Hi Brooke.

 

When you want to find inverse functions, simply swap out every y with every x, and then solve for y.

 

y = 3/(x-5) - 2

 

To find this function's inverse, replace x with y and y with x.

 

x = 3/(y-5) - 2

 

Now solve for y.

 

x + 2 = 3/(y-5)

 

1/(x+2) = (y-5)/3

 

3/(x+2) = y-5

 

y = 3/(x+2) + 5

 

This is your inverse function.

 

f^-1(x) = 3/(x+2) + 5

 

Hope this helps.