Problem
Select your answer (17 out of 25$)$ If $f(x)=2 x^{2}-2$ and $g(x)=2 x+1$, evaluate $f(g(x))$ when $x=-3$
Solution
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 \(\boxed{48}\).
