Question

Catherine claims that each of the following pairs of functions are inverses. However, ONE of the pairs are NOT inverses. Pick the pair of functions that are NOT actually inverses. f(x)=x/3 1 and f−1(y)=3(y−1) f(x)=4x 16 and f−1(y)=1/4y−16 f(x)=4x 9 and f−1(y)=(y−9)/4 f(x)=3x 9 and f−1(y)=1/3y−3 f(x)=(x 2)/4 and f−1(y)=4y−2

Answer 1

The pair f(x) = 4x and
`f^-1(y) = 1/4y - 16` are not inverses of each other. Option B

To determine which pair of functions are not actually inverses, we need to find the pair where applying one function followed by the inverse does not yield the original input.

The pair of functions that are not inverses is:

f(x) = 4x and
`f^-1(y) = 1/4y - 16`

Let's check the composition of these functions:

`f(f^-1(y)) = f(1/4y - 16)`

= 4 × (1/4y - 16)

= y - 64

This result is not equal to the original input y.

Hence, the pair f(x) = 4x and f^-1(y) = 1/4y - 16 are not inverses of each other.