Problem

Given that $f(x)=2 x+3$ and $g(x)=x^{2}-3 x-4$, find $(g \circ f)(7)$.

Answer

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Answer

So, \((g \circ f)(7) = \boxed{234}\).

Steps

Step 1 ：Given that \(f(x)=2 x+3\) and \(g(x)=x^{2}-3 x-4\), we need to find \((g \circ f)(7)\).

Step 2 ：This means we first apply the function \(f(x)\) to our input, and then apply the function \(g(x)\) to the result.

Step 3 ：First, find \(f(7)\). Substituting \(x = 7\) into \(f(x)\), we get \(f(7) = 2*7 + 3 = 17\).

Step 4 ：Next, substitute this result into \(g(x)\) to find \((g \circ f)(7)\). So, \(g(f(7)) = g(17) = 17^2 - 3*17 - 4 = 234\).

Step 5 ：So, \((g \circ f)(7) = \boxed{234}\).

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