Find $f^{-1}$ of $f(x)= \frac{x}{9}-5$.

Question

what is answer

Answer 1

Hi Mae.

 

If I am interpreting the LaTEX right, I think your math problem is restated as:

 

Find f^-1 of f(x) = x/9 - 5

 

To find the inverse, replace all x's with y's and replace all y's with x's.  Then solve for y.

 

 

Here, we would rewrite  f(x) as "y" and start with y = (x/9) - 5

 

Now swap x's and y's to get   x = (y/9) - 5

 

Now solve for y.

 

Add 5 to both sides

 

x + 5 = y/9

 

 

Multiply both WHOLE SIDES by 9

 

9(x+5) = y    or   y = 9x+45

 

 

So this new "y" is your inverse function and the answer is 

 

f^-1(x) = 9x + 45