Problem

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

Answer

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Answer

\(\boxed{(g \circ f)(-1) = 17}\)

Steps

Step 1 ：Substitute \(-1\) into the function \(f(x)\): \(f(-1) = 3(-1) - 1 = -3 - 1 = -4\)

Step 2 ：Substitute the result from step 1, which is \(-4\), into the function \(g(x)\): \(g(-4) = (-4)^2 + 1 = 16 + 1 = 17\)

Step 3 ：\(\boxed{(g \circ f)(-1) = 17}\)

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