Answer
f[g(-2)] = 42
Step-by-step explanation
To find f[g(-2)], first, we need to find g(-2).
To find g(-2) we have to substitute x = -2 into the function g(x), as follows:
[tex]\begin{gathered} g(x)=3x+1 \\ g(-2)=3\cdot(-2)+1 \\ g(-2)=-6+1 \\ g(-2)=-5 \end{gathered}[/tex]
In consequence, f[g(-2)] is equivalent to:
[tex]f\lbrack g(-2)]=f(-5)[/tex]
To find f(-5) we have to substitute x = -5 into the function f(x), as follows:
[tex]\begin{gathered} f(x)=2x^2-8 \\ f(-5)=2(-5)^2-8 \\ f(-5)=2\cdot25-8 \\ f(-5)=50-8 \\ f(-5)=42=f\lbrack g(-2)] \end{gathered}[/tex]
