If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

To start, distribute the expression (g - f) applied to 3, which results in g(3) - f(3). Our task is to find these values by substituting 3 into each function.

Calculate f(3): f(3) = 4 - 2(3) = 4 - 6 = -2
Calculate g(3): g(3) = 6 * 3 = 18
Now that we have f(3) and g(3), substitute back into the expression: g(3) - f(3) = 18 - (-2) = 18 + 2 = 20.
Next, we need to simplify each answer choice to identify which equals 20.
A: 6 - 3 - (4 + 3) * 2 = 6 - 3 - (7 * 2) = 3 - 14 = -11
B: 6 - 3 - (4 - 32) = 6 - 3 - (-28) = 3 + 28 = 31
C: (6)(3) - 4 + 32 = 18 - 4 + 32 = 46
D: 6(3) - 4 - 32 = 18 - 4 - 32 = -18
Surprisingly, none of the choices match the value 20. There may be a mistake in the problem as provided. Double-check for typos or ask your teacher for clarification. Hope this explanation helps! :D

Answer:

 

Detailed explanation:

Starting with the given functions,

Then,

        ( Subtracting the functions )

          ( Using equations (1) and (2) )

             ( Applying the associative property )

The third choice is the correct one.