Question

Let h(x) = -2x2 + 9 and g(x) = x/5. Perform the operation (h • g)(-5).

Answer 1

7

Explanation:

(h • g)(x) is a composite function, which essentially means that we are looking for h(g(x)), where g(x) replaces x in the function h(x).

We know that h(x) =
`-2x^2+9` and g(x) = x/5. We want: h(g(x)) =
`-2(g(x))^2+9`. So, just plug x/5 in for g(x):
`h(g(x))=-2(x/5)^2+9=-2(x^2/25)+9=(-2)/(25) x^2+9`

Now, since we want h(g(-5)), we plug -5 in for x: h(g(-5)) =
`(-2)/(25) (-5)^2+9=(-2)/(25)*25+9=-2 +9=7`

Thus, the answer is 7.

Hope this helps!