Question

Which of the following is the inverse of f(x)

Answer 1

`(4x^2-1)/(2)`

Explanation:

To find the inverse set f(x) = x and replace every x term on the right to a y. Then solve for y.

`f(x) = (1)/(2)` ×
`√(2x+1)`

`x=(1)/(2) (2y+1)^(1)/(2)` - Re-write the square root using power.

`2x=(2y+1)^(1)/(2)` - Multiply by 2

`(2x)^2 =2y+1` - Square both sides to get rid of the square root.

`4x^2 - 1 = 2y` - Multiply out the bracket and take one from both sides.

`(4x^2-1)/(2) = y`

Now set y as the inverse of f(x).