Question

Consider the function.

3
f(x) = -X + 12
4
What is the y-intercept of f'(x)?
-16
ООО
- 12
3
4

Answer 1

A. -16

Explanation:

Note that
`f^(-1)(x)` stands for the inverse of
`f(x)`. We can write the graph as
`y=(3)/(4)x+12`. Switching
`y` with
`x` and vice versa will now get us the inverse of the graph, so we see that the inverse is
`x=(3)/(4)y+12`.

We are asked for the y-intercept, which is the point for which
`x=0`. Substituting that gives
`0=(3)/(4)y + 12` or
`(3)/(4)y = -12`, so
`y=-12\cdot (4)/(3) = -16.` We are now done.