Question

Consider functions fand g.f(x)g(x)Which expression is equal to f(x) · g(x)?==√x² + 12x + 36x312O A. x4 + 6x³OB. 4-OC. x4--OD. 7x³ --6x³--12x12x³ + 6x-12x + 7212x - 7272-72

Answer 1

Given:

The function

$\begin{gathered} f(x)=\sqrt{x^2+12x+36} \\ g(x)=x^3-12 \end{gathered}$

Required:

$\text{ Which expression is equal to }f(x)\cdot g(x)?$

Explanation:

The calculation is as:

$\begin{gathered} \text{ We can write }f(x)\text{ as }:\text{ } \\ f(x)=\sqrt{x^2+12x+36} \\ =\sqrt{(x+6)^2} \\ =x+6 \end{gathered}$

Now,

$\begin{gathered} f(x)\cdot g(x)=(x+6)(x^3-12) \\ =x^4-12x+6x^3-72 \\ =x^4+6x^3-12x-72 \end{gathered}$

Answer: