finding the inverse

Question

Given the function f(x)=9x+7, find the inverse.

 

Please help me find the inverse...

Answer 1

To find the inverse of a function remember that a function's inverse is a function g such that for all x f(g(x))=x and g(f(x))=x

Start with setting y = 9x+7, and solve for y:

First subtract 7 from both sides: y-7=9x 

Now divide both sides by 9: (y-7)/9=x

Let g(x) = (x-7)/9.  Consider f(g(x))= 9((x-7)/9)+7 = 9/9(x-7)+7 = (x-7)+7 = x

You can check for yourself that g(f(x))=x as well.

Hope this is helpful.