Question

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

Answer 1

`\displaystyle (fg)(-(1)/(5))=0`

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)(-(1)/(5))`

This is equivalent to:

`\displaystyle =f(-(1)/(5))g(-(1)/(5))`

By substitution:

`\displaystyle f(-(1)/(5))=(-(1)/(5))^2-13=(1)/(25)-13=-(324)/(25)`

And:

`\displaystyle g(-(1)/(5))=5(-(1)/(5))+1=-1+1=0`

Hence:

`\displaystyle =(-(324)/(25))(0)=0`

Our final answer is:

`\displaystyle (fg)(-(1)/(5))=0`