Answer:
7
Step-by-step 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) = [tex]-2x^2+9[/tex] and g(x) = x/5. We want: h(g(x)) = [tex]-2(g(x))^2+9[/tex]. So, just plug x/5 in for g(x): [tex]h(g(x))=-2(x/5)^2+9=-2(x^2/25)+9=\frac{-2}{25} x^2+9[/tex]
Now, since we want h(g(-5)), we plug -5 in for x: h(g(-5)) = [tex]\frac{-2}{25} (-5)^2+9=\frac{-2}{25}*25+9=-2 +9=7[/tex]
Thus, the answer is 7.
Hope this helps!
