The Solution:
The given function is

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

Dividing both sides by 4, we get

So, the inverse of f(x) is

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

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