Verified answer

g(x) = (x + 4)/3

or ... g(x) = (1/3)x + 4/3

If f(g(x))=x, that the functions are inverses. To find g(x), instead of figuring out what you need to plug into f(x), you can figure out what you need to plug f(x) into to get x (solve g(f(x))=x).

First, we need to set up an equation. Since f(x) is linear, g(x) also has to be linear.

f(x)=3x-4

g(x)=mx+b

g(f(x))= m(3x-4)+b=x

Now, we can just expand and solve:

m(3x-4)+b=x

3mx-4m+b=x

Divide the equation into two parts

3mx=x -4m+b=0

3m=1

m=1/3

-4(1/3)+b=0

b=4/3

This means that g(x)=1/3x+4/3