Question

From the graph of f and g , in the figure, we find

$\begin{array}{c}\left(f+g\right)\left(2\right)=\_\_\_\_\_\\ \left(f-g\right)\left(2\right)=\_\_\_\_\_\\ \left(fg\right)\left(2\right)=\_\_\_\_\_\\ \left(\frac{f}{g}\right)\left(2\right)=\_\_\_\_\_\end{array}$

Short answer

The required values are
$\left(f+g\right)\left(2\right)=8,\left(f-g\right)\left(2\right)=-2,\left(fg\right)\left(2\right)=15$and$\left(\frac{f}{g}\right)\left(2\right)=0.6$

Step-by-step solution

– Given information.

The given graph is:

From the above graph it is clear that $f\left(2\right)=3$and $g\left(2\right)=5$

–Find the sum of two functions at 2.

$\begin{array}{c}\left(f+g\right)\left(x\right)=f\left(x\right)+g\left(x\right)\\ \left(f+g\right)\left(2\right)=f\left(2\right)+g\left(2\right)\\ =3+5\\ =8\end{array}$

– Find the difference of two functions at 2.

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

– Find the product of two functions at 2.

$\begin{array}{c}\left(fg\right)\left(x\right)=f\left(x\right)\cdot g\left(x\right)\\ \left(fg\right)\left(2\right)=f\left(2\right)\cdot g\left(2\right)\\ =3\cdot 5\\ =15\end{array}$

– Find the quotient of two functions at 2.

$\begin{array}{c}\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}\\ \left(\frac{f}{g}\right)\left(2\right)=\frac{f\left(2\right)}{g\left(2\right)}\\ =\frac{3}{5}\\ =0.6\end{array}$

Thus, the required values are $\left(f+g\right)\left(2\right)=8,\left(f-g\right)\left(2\right)=-2,\left(fg\right)\left(2\right)=15$and $\left(\frac{f}{g}\right)\left(2\right)=0.6$