Problem

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

Solution

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 \(y = \sqrt{\frac{x - 5}{3}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/GIHhPfbr36/

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