Question

Find the inverse of f(x) = 12x - 3

Answer 1

ANSWER

$f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}$

EXPLANATION

We want to find the inverse of the function given:

f(x) = 12x - 3

First, replace f(x) with y:

y = 12x - 3

Now, make x the subject of the function:

y + 3 = 12x

$\begin{gathered} \Rightarrow\text{ x = }\frac{y}{12}\text{ + }\frac{3}{12} \\ x\text{ = }\frac{y}{12}\text{ + }\frac{1}{4} \end{gathered}$

Now, replace x with f-1(x) and y with x:

$f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}$

That is the inverse function.