Question

Find the inverse of the function. f(x) = 6x3 + 3

Answer 1

The answer is   $f^{-1}(x) = \sqrt[3]{ \frac{x-3}{6}}$

Our function is f(x) = 6x³ + 3. We need to find f⁻¹(x)
Step 1: Substitute y for f(x):
            y = 6x³ + 3
Step 2: Switch x and y because every (x, y) has its partner (y, x):
            x = 6y³ + 3 
Step 3: Solve for y:
                      $6y^{3} =x-3 \\ y^{3}= \frac{x-3}{6} \\ y = \sqrt[3]{ \frac{x-3}{6}}$
        $f^{-1}(x) = \sqrt[3]{ \frac{x-3}{6}}$