Question

If f(x) = 3x2, find the inverse of f.

Answer 1

Answer:

The inverse of f is

$y = \sqrt{ \frac{x}{3} }$

Step-by-step explanation:

f(x) = 3x²

To find the inverse of f equate f(x) to y

That's f(x) = y

We have

y = 3x²

Interchange the terms

x = 3y²

Make y the subject

x = 3y²

Divide both sides by 3

${y}^{2} = \frac{x}{3}$

Find the square root of both sides to make y stand alone

That's

$\sqrt{ {y}^{2} } = \sqrt{ \frac{x}{3} }$

The final answer is

$y = \sqrt{ \frac{x}{3} }$

Hope this helps you