Question

Given that f(x)=x^2-13 and g(x)=5x+1, find (fg)(-1/5)

Answer 1

Answer:

$\displaystyle (fg)(-\frac{1}{5})=0$

Step-by-step explanation:

We are given the two functions:

$f(x)=x^2-13\text{ and } g(x)=5x+1$

And we want to find:

$\displaystyle (fg)(-\frac{1}{5})$

This is equivalent to:

$\displaystyle =f(-\frac{1}{5})g(-\frac{1}{5})$

By substitution:

$\displaystyle f(-\frac{1}{5})=(-\frac{1}{5})^2-13=\frac{1}{25}-13=-\frac{324}{25}$

And:

$\displaystyle g(-\frac{1}{5})=5(-\frac{1}{5})+1=-1+1=0$

Hence:

$\displaystyle =(-\frac{324}{25})(0)=0$

Our final answer is:

$\displaystyle (fg)(-\frac{1}{5})=0$