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