Question

Find the inverse of the function f(x)=6x^2+3

Answer 1

The answer is

`{f}^( - 1) (x) = \sqrt{ (x - 3)/(6) }`

Explanation:

f(x) = 6x² + 3

To find the inverse of the function above equate it to y

That's

f(x) = y

So we have

y = 6x² + 3

Next interchange the variables that's x becomes y and y becomes x.

x = 6y² + 3

Next make y the subject

Subtract 3 from both sides

That's

6y² + 3 - 3 = x - 3

6y² = x - 3

Divide both sides by 6

That's

`{y}^(2) = (x - 3)/(6)`

Next find the square root of both sides

`y = \sqrt{ (x - 3)/(6) }`

We have the final answer as

`{f}^( - 1) (x) = \sqrt{ (x - 3)/(6) }`

Hope this helps you