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

Answer:

h(x) = x^3.

Step-by-step explanation:

h(x) = x^3

because (h o g)(x)  = (6x^3 - 7)^3.

Answer 2

Answer:

h(x) = x³

Step-by-step explanation:

$\text{We can notice:}$

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

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