How to do these problems? I'm stuck...?

Question

Find the following:

Ex. g(8) = 6(8^2) + 1/8

1) g(s+h)

(replace 8 by plug in s+h)

2) g(s+h) - g(s)

Given the function below, evaluate the following expressions:

h(r) = 9 / r+4

1) h(x^2)+1 (plug in this to replace r)

Answer 1

g(8) = 6(8^2) + 1/8

so g(s+h) = 6((s+h)^2) + 1/(s+h)

Do you see what I did?  I substituted (s+h) for 8 in the function definition.  But we're not done yet, because we need to reduce the expression:

g(s+h) = 6(s^2 + 2sh +h^2) + 1/(s+h)

or by multiplying the first term by (s+h)/(s+h)

g(s+h) = (6s^3 + 18s^2h + 18sh^2 +6h^3 + 1)/(s+h)

For question 2, g(s) = 6s^2 + 1/s.  Subtract this from the answer above and reduce.

For the next question, substitute x^2 for r in the function definition:

h(x^2) = 9/(x^2 + 4)

so h(x^2)+1 = 9/(x^2 + 4) + 1, but we still need to reduce:

h(x^2)+1 = 9/(x^2 + 4) + (x^2 + 4)/(x^2 + 4)

h(x^2)+1 = (x^2 + 13) / (x^2 + 4)