Answer:
[tex]\displaystyle (f\cdot g)(1) = 0[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=x^2-1\text{ and } g(x)=\sqrt x[/tex]
And we want to find:
[tex](f\cdot g)(1)[/tex]
Recall that this is equivalent to:
[tex](f\cdot g)(1) =f(1)\cdot g(1)[/tex]
Evaluate each function individually:
[tex]\displaystyle \begin{aligned} f(1) & = (1)^2 - 1 \\ \\ & = 1 - 1 \\ \\ & = 0 \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned} g(1) & = \sqrt{(1)} \\ \\ & = 1 \end{aligned}[/tex]
Hence substitute and evaluate:
[tex]\displaystyle \begin{aligned} (f\cdot g)(1) & = f(1) \cdot g(1) \\ \\ & = (0) \cdot (1) \\ \\ & = 0\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (f\cdot g)(1) = 0[/tex]
