1 Answer

Venkatskpi · Answer 1 · 2022-03-27T16:39:20+0000

Answer:

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

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:

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

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