Question

what is the inverse of f(x) =x/12 +15

Answer 1

The given function is

$f(x)=\frac{x}{12}+15$

To find the inverse of this function, we have to isolate x.

$y=\frac{x}{12}+15$

First, we subtract 15 on each side

$\begin{gathered} y-15=\frac{x}{12}+15-15 \\ y-15=\frac{x}{12} \end{gathered}$

Then, we multiply 12 on each side

$\begin{gathered} 12(y-15)=12\cdot\frac{x}{12} \\ 12y-180=x \end{gathered}$

Now, we exchange the variables, that is, we change x for y, and we change y for x.

$y=12x-180$

Therefore, the inverse is

$f(x)^{-1}=12x-180$