Question

Find (f•g)(1) f(x)= x^2-1 g(x)=sqrt x

Answer 1

`\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`