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).

examine the two-step equation.

−  

7

4

+  

x

4

= 2

which property of operations allows you to add the same constant term to both sides?

multiplication property of equality

division property of equality

addition property of equality

subtraction property of equality

step-by-step explanation: