Problem

Given the functions \(f(x) = 3x - 7\) and \(g(x) = 2x^2 + 1\), find the value of \(f(g(2))\).

Answer

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Answer

Next, we substitute \(g(2)\) into the equation for \(f(x)\): \(f(g(2)) = f(9) = 3(9) - 7 = 27 - 7\).

Steps

Step 1 ：First, we need to find the value of \(g(2)\). To find this, we substitute \(x = 2\) into the equation for \(g(x)\): \(g(2) = 2(2)^2 + 1 = 2(4) + 1 = 8 + 1 = 9\).

Step 2 ：Next, we substitute \(g(2)\) into the equation for \(f(x)\): \(f(g(2)) = f(9) = 3(9) - 7 = 27 - 7\).

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