A rectangle has a length represented by the function f(x)=x and a width represented by the function g(x)=x+3 where both functions are in feet

Question

Calculate (f•g)(x) and stare what it represents

Answer 1

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

Given:

• \(f(x) = x\) (the length of the rectangle)
• \(g(x) = x + 3\) (the width of the rectangle)

The product of the two functions is calculated as follows:

\[ (f \cdot g)(x) = f(x) \cdot g(x) = x \cdot (x + 3) \]

Now, we can simplify the expression:

\[ (f \cdot g)(x) = x \cdot (x + 3) = x^2 + 3x \]

This expression, \(x^2 + 3x\), represents the area \(A\) of the rectangle as a function of \(x\), where \(x\) is the length and \(g(x)\) is the width of the rectangle.

Thus, the interpretation is:

\[ A(x) = x^2 + 3x \text{ square feet} \]

This means that for a rectangle with length \(x\) feet and width \(x + 3\) feet, the area can be expressed as \(x^2 + 3x\) square feet.