Question

Consider these functions:

Answer 1

Answer:

The value of f(g(-2)) is 12.

Step-by-step explanation:

We'll start by solving g(-2):

$g(-2)\\= (-2)^2 + 2\\= 4 + 2\\= 6$

Now we can take that value and plug it into function f:

$f(6)\\= \frac{-1}{2}6^2 + 5 * 6\\= -36/2 + 30\\= -18 + 30\\= 12$

Alternatively, you can work out a new single function that in itself describes f(g())

$f(g(x)) = -\frac{1}{2}g(x)^2 + 5g(x)\\= -\frac{1}{2}(x^2 + 2)^2 + 5(x^2 + 2)\\= -\frac{1}{2}(x^4 + 4x^2 + 4) + 5x^2 + 10\\= -\frac{1}{2}x^4 - 2x^2 - 2 + 5x^2 + 10\\= -\frac{x^4}{2} + 3x^2 + 8$

and try plugging -2 into the new function

$= - \frac{-2^4}{2} + 3(-2)^2 + 8\\= -16 / 2 + 3 * 4 + 8\\= -8 + 12 + 8\\= 12$

Answer 2

Answer:

The answer is 12

Step-by-step explanation: