Chapter 9.9, Problem 47PPS

To determine

To describe sometime, always or never true.

Answer to Problem 47PPS

Sometimes

Explanation of Solution

Given information:

  $(f•g)(x)$

The Product of Two Functions

Suppose we have two functions, $f(x)$ and $g(x)$ . We can define the product of these two functions by,

  $(f•g)(x)=f(x)•g(x)$

where x is in the domain of both f and g .

For example, we can multiply the functions $f(x)=(x+1)$ and $g(x)=(x+2)$ as,

equation:

  $(f•g)(x)=f(x)•g(x)$

On solving,

  $=(x+1)•(x+2)$

On solving,

  $(f•g)(x)=(x^2+3x+2)$

When $f(x)$ and $g(x)$are linear functions

Then,

  $(f•g)(x)$ will be quadratic

But when $f(x)$ and $g(x)$are not linear functions

Then,

  $(f•g)(x)$ will not be quadratic

Hence, $(f•g)(x)$ will be quadratic sometimes