Answer:
[tex]\displaystyle f[g(2)] = 3[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = -2x - 1\text{ and } g(x) = -x[/tex]
And we want to find the value of:
[tex]\displaystyle f[g(2)][/tex]
First, evaluate g(2):
[tex]\displaystyle \begin{aligned} g(2) &= -(2) \\ &= -2\end{aligned}[/tex]
Substitute:
[tex]\displaystyle f[g(2)] = f(-2)[/tex]
Evaluate f(-2):
[tex]\displaystyle \begin{aligned} f(-2) &= -2(-2) - 1 \\ &= 4 - 1 \\ &= 3\end{aligned}[/tex]
Therefore:
[tex]\displaystyle f[g(2)] = 3[/tex]
