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)


What is the situation described by (f *g) (x) ?

Answer 1

To calculate \((f \cdot g)(x)\), we first find the product of the two functions \(f(x)\) and \(g(x)\). The functions are defined as:

- \(f(x) = x\) (the length of the sandbox in yards)
- \(g(x) = x + 6\) (the width of the sandbox in yards)

Now, we multiply the two functions:

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

Now, let's simplify this expression:

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

So, \((f \cdot g)(x) = x^2 + 6x\).

### Situation Described by \((f \cdot g)(x)\)

The expression \((f \cdot g)(x) = x^2 + 6x\) represents the area of the sandbox in square yards, where \(x\) is the length of the sandbox in yards and \(g(x) = x + 6\) is the width.

In this scenario:

- \(x\) is the length of the sandbox,
- \(x + 6\) is the width of the sandbox,
- The area of the sandbox is calculated by multiplying the length and width together, resulting in the expression \(x^2 + 6x\).

Thus, \((f \cdot g)(x)\) describes the area of a rectangular sandbox where the length is \(x\) yards and the width is \(x + 6\) yards.