Question

Consider these functions:

f(x)=-1/2x²+5
g(x)= x²+2
What is the value of f(g(-2))?
A. -28
B. -12
C.12
D. 146

Answer 1

The value of f(g(-2)) is found by first evaluating g(-2), which is 6, and then using this result to evaluate f(6). The final result is -13, which is not in the provided options.

Step-by-step explanation:

To find the value of f(g(-2)), you first need to calculate g(-2) and then evaluate f at the result of g(-2).

Step 1: Evaluate g(-2)

Given g(x) = x² + 2, plug -2 in for x:

g(-2) = (-2)² + 2 = 4 + 2 = 6

Step 2: Evaluate f(g(-2)) or f(6)

Now, take the result from step 1 and plug it into the function f:

Given f(x) = -1/2x² + 5, plug 6 in for x:

f(6) = -½(6)² + 5 = -½(36) + 5 = -18 + 5 = -13

Therefore, the value of f(g(-2)) is -13, which is not listed in the provided multiple-choice options.