Answer:
[tex]\displaystyle (fg)(-\frac{1}{5})=0[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=x^2-13\text{ and } g(x)=5x+1[/tex]
And we want to find:
[tex]\displaystyle (fg)(-\frac{1}{5})[/tex]
This is equivalent to:
[tex]\displaystyle =f(-\frac{1}{5})g(-\frac{1}{5})[/tex]
By substitution:
[tex]\displaystyle f(-\frac{1}{5})=(-\frac{1}{5})^2-13=\frac{1}{25}-13=-\frac{324}{25}[/tex]
And:
[tex]\displaystyle g(-\frac{1}{5})=5(-\frac{1}{5})+1=-1+1=0[/tex]
Hence:
[tex]\displaystyle =(-\frac{324}{25})(0)=0[/tex]
Our final answer is:
[tex]\displaystyle (fg)(-\frac{1}{5})=0[/tex]
