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If $f(x)=2 x^{2}-2$ and $g(x)=2 x+1$, evaluate $f(g(x))$ when $x=-3$

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Final Answer: The value of the function $f(g(x))$ when $x=-3$ is $\boxed{48}$.

Steps

Step 1 ：Given the functions $f(x)=2 x^{2}-2$ and $g(x)=2 x+1$, we are asked to evaluate $f(g(x))$ when $x=-3$.

Step 2 ：First, we find the value of $g(-3)$. Substituting $-3$ into $g(x)$, we get $g(-3) = 2(-3) + 1 = -5$.

Step 3 ：Next, we substitute this value into the function $f(x)$. So, $f(g(-3)) = f(-5)$.

Step 4 ：Substituting $-5$ into $f(x)$, we get $f(-5) = 2(-5)^{2} - 2 = 48$.

Step 5 ：Final Answer: The value of the function $f(g(x))$ when $x=-3$ is $\boxed{48}$.