I need to find the composite of two fuctions. The Problem is (H of G)(X). F(x)=X^2-1, G(x)=3X.?

Question

The Answer is 6-X^2. But I cannot find it for the life of me. Help?

Answer 1

F(x)=X^2-1, G(x)=3X, and you want F(G(x))?

First, avoid confusion, and rewrite them as

F(u)=u^2-1, G(v)=3v, no x's.

Note what F does: squares the input u, less 1.

Note what G does: multiplies input v by 3, right?

Now, back to the x's. G(x) = 3x.

F(G(x)) = F(3x). What does F do? squares input, less 1.
= (3x)^2 -1 or
= 9x^2 -1.

Your answer is wrong, by the way, even if you take G(F(x)).

Answer 2

If you mean f(g(x)), then it
= (3x)^2 -1 = 9x^2 -1

If you mean g(f(x)) then it
= 3(x^2-1) = 3x^2-1

Perhaps you could tell us what h(x) is. If h(x) were 6-(x/3)^2, then h(g(x)) = 6-x^2