Chapter 1.2, Problem 5CFU

To determine

To find: $f\left(x\right)+g\left(x\right),f\left(x\right)-g\left(x\right),f\left(x\right)\cdot g\left(x\right)\text{ and }\frac{f}{g}\left(x\right)$ .

Answer to Problem 5CFU

  $\begin{array}{c}f\left(x\right)+g\left(x\right)=3x^2+6x+4\\ f\left(x\right)-g\left(x\right)=3x^2+2x-14\\ f\left(x\right)\cdot g\left(x\right)=6x^3+35x^2+26x-45\\ \frac{f}{g}\left(x\right)=\frac{\left(3x^2+4x-5\right)}{\left(2x+9\right)}\end{array}$

Explanation of Solution

Given information: The functions given are as follows:

  $\begin{array}{l}f\left(x\right)=3x^2+4x-5\\ g\left(x\right)=2x+9\end{array}$

Calculation:

To find $f\left(x\right)+g\left(x\right)$ , put the values of $f\left(x\right)$ and $g\left(x\right)$ in $f\left(x\right)+g\left(x\right)$ and simplify as follows:

  $\begin{array}{c}f\left(x\right)+g\left(x\right)=\left(3x^2+4x-5\right)+\left(2x+9\right)\\ =3x^2+6x+4\end{array}$

Thus, the value of $f\left(x\right)+g\left(x\right)$ is $3x^2+6x+4$ .

Similarly, put the values of $f\left(x\right)$ and $g\left(x\right)$ in $f\left(x\right)-g\left(x\right)$ and simplify as follows:

  $\begin{array}{c}f\left(x\right)-g\left(x\right)=\left(3x^2+4x-5\right)-\left(2x+9\right)\\ =3x^2+2x-14\end{array}$

Thus, the value of $f\left(x\right)-g\left(x\right)$ is $3x^2+2x-14$ .

Similarly, put the values of $f\left(x\right)$ and $g\left(x\right)$ in $f\left(x\right)\cdot g\left(x\right)$ and simplify as follows:

  $\begin{array}{c}f\left(x\right)\cdot g\left(x\right)=\left(3x^2+4x-5\right)\cdot \left(2x+9\right)\\ =6x^3+27x^2+8x^2+36x-10x-45\\ =6x^3+35x^2+26x-45\end{array}$

Thus, the value of $f\left(x\right)\cdot g\left(x\right)$ is $6x^3+35x^2+26x-45$ .

Similarly, put the values of $f\left(x\right)$ and $g\left(x\right)$ in $\frac{f}{g}\left(x\right)$ and simplify as follows:

  $\frac{f}{g}\left(x\right)=\frac{\left(3x^2+4x-5\right)}{\left(2x+9\right)}$

Thus, the value of $\frac{f}{g}\left(x\right)$ is $\frac{\left(3x^2+4x-5\right)}{\left(2x+9\right)}$ .