The functions f(x) and g(x) are defined below. which expression is equal to f(x) · g(x)?

none of the above

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

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).

109 is the nearest whole number/final answer! : )

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day