Question

If f(x)=4x-2, what is the y intercept of the inverse of f(x)?

Answer 1

The Solution:

The given function is

$y=f(x)=4x-2$

So, to find the inverse of f(x), we shall make x the subject of the formula.

$\begin{gathered} y=4x-2 \\ \text{ Adding 2 to both sides, we get} \\ y+2=4x-2+2 \\ y+2=4x \end{gathered}$

Dividing both sides by 4, we get

$\begin{gathered} \frac{4x}{4}=\frac{y+2}{4} \\ \\ x=\frac{y+2}{4} \end{gathered}$

So, the inverse of f(x) is

$f^{-1}(x)=\frac{x+2}{4}$

The y-intercept of the inverse of f(x) is the value of the inverse of f(x) when x=0

Substituting 0 for x in the inverse of f(x), we have

$f^{-1}(0)=\frac{0+2}{4}=\frac{2}{4}=\frac{1}{2}$

So, the y-intercept of the inverse of f(x) is 1/2

Therefore, the correct answer is 1/2.