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} (4x)/(4)=(y+2)/(4) \\ \\ x=(y+2)/(4) \end{gathered}`

So, the inverse of f(x) is

`f^(-1)(x)=(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)=(0+2)/(4)=(2)/(4)=(1)/(2)`

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

Therefore, the correct answer is 1/2.