Question

The functions f(x) and g(x) are defined below. f(x)=sq. root x^2+12x+36 g(x)=x^3-12 Which expression is equal to f(x) · g(x)?

Answer 1

Answer: $\bold{x^4+6x^3-12x-72}$

Step-by-step explanation:

$f(x) = \sqrt{x^2+12x+36} \implies f(x)=\sqrt{(x+6)^2}\implies f(x) = x+6\\\\\\f(x)\cdot g(x)=(x+6)(x^3-12)\\.\qquad \qquad =x(x^3-12)+6(x^3-12)\\.\qquad \qquad =x^4-12x +6x^3-72\\.\qquad \qquad =\large\boxed{x^4+6x^3-12x-72}$

Answer 2

The expression equal to f(x)·g(x) is  $x^{4} + 6x^{3} - 12x - 72$ .

What is the equivalent expression of f(x)·g(x) after simplification ?

The expressions given are f(x) = $\sqrt{x^{2}+12x+36}$  and g(x) = $x^{3} - 12$ .

Thus we have

⇒ f(X) = $\sqrt{x^{2}+12x+36}$

⇒ f(x) = $\sqrt{(x+6)^{2} }$

⇒ f(x) = x + 6 .

Therefore the expression of multiplication of f(x)·g(x) is =

= $(x^{3} - 12)*(x + 6)$

= $x^{4} + 6x^{3} - 12x - 72$

Thus, the expression equal to f(x)·g(x) is  $x^{4} + 6x^{3} - 12x - 72$ .

To learn more about simplification of expression, refer -

https://brainly.com/question/723406

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