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Find (f•g)(1) f(x)= x^2-1 g(x)=sqrt x

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Answer:


\displaystyle (f\cdot g)(1) = 0

Explanation:

We are given the two functions:


f(x)=x^2-1\text{ and } g(x)=\sqrt x

And we want to find:


(f\cdot g)(1)

Recall that this is equivalent to:


(f\cdot g)(1) =f(1)\cdot g(1)

Evaluate each function individually:


\displaystyle \begin{aligned} f(1) & = (1)^2 - 1 \\ \\ & = 1 - 1 \\ \\ & = 0 \end{aligned}

And:


\displaystyle \begin{aligned} g(1) & = √((1)) \\ \\ & = 1 \end{aligned}

Hence substitute and evaluate:


\displaystyle \begin{aligned} (f\cdot g)(1) & = f(1) \cdot g(1) \\ \\ & = (0) \cdot (1) \\ \\ & = 0\end{aligned}

In conclusion:


\displaystyle (f\cdot g)(1) = 0

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