Question

Let f(x) = (6x^3 – 7)^3 and g(x) = 6x^3 - 7.
Given that f(x) = (hog)(x), find h(x).

Answer 1

h(x) = x³

Explanation:

`\text{We can notice:}`

`g(x)=6x^3-7,\ f(x)=(\underbrace{6x^3-7}_(g(x)))^3=\bigg(g(x)\bigg)^3`

`\text{If}\ f(x)=(h\circ g)(x)=h\bigg(g(x)\bigg),\ \text{then}\ h(x)=x^3`

Answer 2

h(x) = x^3.

Explanation:

h(x) = x^3

because (h o g)(x) = (6x^3 - 7)^3.