Problem

Find the inverse of the function \(f(x) = 3x^2 + 5\)

Answer

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Answer

Step 5: Finally, take the square root of both sides to get \(y = \sqrt{\frac{x - 5}{3}}\)

Steps

Step 1 ：Step 1: Replace \(f(x)\) with \(y\), so that the equation becomes \(y = 3x^2 + 5\)

Step 2 ：Step 2: Swap \(x\) and \(y\), so that the equation becomes \(x = 3y^2 + 5\)

Step 3 ：Step 3: Solve for \(y\). First, subtract 5 from both sides to get \(x - 5 = 3y^2\)

Step 4 ：Step 4: Then, divide both sides by 3 to get \(\frac{x - 5}{3} = y^2\)

Step 5 ：Step 5: Finally, take the square root of both sides to get \(y = \sqrt{\frac{x - 5}{3}}\)

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