Chapter 9.9, Problem 49HP

To determine

Solve the function.

Answer to Problem 49HP

Yes

Explanation of Solution

Given Information: $f\left(x\right)$ and

  $g\left(x\right)$ are linear function.

Formula Used: $\left(f·g\right)\left(x\right)=f(x)·g\left(x\right)$

Calculation:

  $f\left(x\right)$ and $g\left(x\right)$ are linear function.

  $f\left(x\right)=3x-2$ and $g\left(x\right)=4x+1$

Now, Use formula

  $\left(f·g\right)\left(x\right)=f(x)·g\left(x\right)$

Now, put the value of $f(x)$ and $g(x)$

  $\left(f·g\right)\left(x\right)=\left(3x-2\right)·\left(4x+1\right)$

Now,

  $\left(f·g\right)\left(x\right)=12x^2+3x-8x-2$

Hence,

  $\left(f·g\right)\left(x\right)=12x^2-5x-2$

Yes. If $f\left(x\right)$ and $g\left(x\right)$ are linear function then $\left(f·g\right)\left(x\right)$ cannot be a linear function.

If $f\left(x\right)$ and $g\left(x\right)$ are linear function then $\left(f·g\right)\left(x\right)$ becomes a quadratic function.