f(x)=4x+6; g(x)=x/4-6 is the function inverse of eachother.
$\displaystyle \begin{aligned}
f(x) &= 4x+6 \\
g(x) &= \dfrac{x}{4} - 6
\end{aligned}$
I guess you want to know if f(x) and g(x) are inverses of each other? If
f(g(x)) = x and g(f(x)) = x then the answer is yes.
I'll setup both for you.
$\displaystyle f(g(x))= 4\left( \dfrac{x}{4} - 6 \right) + 6$
...
Will f(g(x)) = x?
And
$\displaystyle g(f(x))= \dfrac{4x + 6}{4} - 6$
...
Will g(f(x)) = x?
The very best way is to take one of the functions and "plug" it into the other
So in this case, $\displaystyle f(x)=4x+6$ and $\displaystyle g(x)=\frac{x}{4}-6$, $\displaystyle f(g(x))$ must equal $\displaystyle x$.
So the inverse of $\displaystyle f(x)=4x+6$ should be:
$\displaystyle g(x)=\frac{x-6}{4}$
Checking that would be:
$\displaystyle f(x)=4(\frac{x-6}{4})+6$
Cancel out the four,
$\displaystyle f(x)=x-6+6$
And simplify,
$\displaystyle f(x)=x$
and so it checks, $\displaystyle g(x)=\frac{x-6}{4}$ is the inverse function.
-Masoug