Question

A sandbox has a length represented by the function f(x) = x which represents the length in yards and g(x) = x + 6 represents the width in yards.

Calculate (f.g) (x) showing your work.

(1 point)

Answer 1

To calculate \((f \cdot g)(x)\), we need to find the product of the two functions \(f(x)\) and \(g(x)\).

Given:
- \(f(x) = x\)
- \(g(x) = x + 6\)

The product of the two functions is given by:

\[
(f \cdot g)(x) = f(x) \cdot g(x)
\]

Substituting the definitions of \(f(x)\) and \(g(x)\):

\[
(f \cdot g)(x) = f(x) \cdot g(x) = x \cdot (x + 6)
\]

Now, we will distribute \(x\) to the expression in the parentheses:

\[
(f \cdot g)(x) = x^2 + 6x
\]

Thus, the result is:

\[
\boxed{x^2 + 6x}
\]