Question

The functions f(x) and g(x) are defined below.

Which expression is equal to f(x) · g(x)?

Answer 1

none of the above

Explanation:

This question wants you to see that the radical can be simplified because it is ...

`f(x)=√((x+6)^2)`

The answer choices show you are expected to simplify this to ...

... f(x) = x +6

Then

... f(x)·g(x) = (x+6)(x³ -12) = x⁴ +6x³ -12x -72 . . . . . matches choice C

_____

However,

... f(x) = |x+6| . . . . . . . √(x^2) = |x|, the positive root regardless of sign of x

so the product f(x)·g(x) only matches selection C for x≥ -6. It matches the opposite of selection C for x ≤ -6.

The attached graph shows this. It graphs f(x), g(x), f(x)·g(x) (as a purple curve), and selection C (as orange dots).