college algebra

Question

g(n)=-3n-5

f(n)=n^2+5n

find (g o f)(n/2)

Answer 1

Hello, thank you for taking the time to post your question!

(g o f)(n/2) means that first you want to find f(n/2), then you can take that value and plug it back into g(n)

for this one that means taking

f(n/2) = (n/2)^2 + 5(n/2)

=0.25n^2 + 2.5n , then plugging that back into g(n)

g(0.25n^2 + 2.5n) = -3(0.25n^2 + 2.5n) - 5

= -0.75n^2 – 7.5n - 5

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

(g°f)(n/2) = g(f(n/2)) = g((n/2)^2 + 5(n/2))

= g(0.25n^2 + 2.5n) = -3(0.25n^2 + 2.5n) -5

= -0.75n^2 -7.5n -5

Which is = -(3/4)n^2 -(15/2)n -5

Either of the last two expressions should be acceptable.