Let f(x) = x^2, g(x)= 2x+5, and h(x)+x^2-1 find g[h(x^3)]

Answer 1

We want to start by finding h(x³). We do this by plugging in x³ for x in h(x). So we get (x³)²-1 = x⁶-1.

Then we plug that for x in g(x). So we are looking for g(x⁶-1).

g(x⁶-1) = 2(x⁶-1)+5 = 2x⁶-2+5 = 2x⁶+3

Answer 2

H(x^3) = x^6-1, replace x by x^3

G[H(x^3) = G(x^6-1) = 2(x^6-1)+5= 2x^6 -2+5 = 2x^6+3