Find the inverse of this function

[utkarshakash]

Homework Statement

Let f be a function defined as f:(0,exp-3/2) → [-1/4, ∞),
$f(x) = (ln x)^2 + 3 ln x + 2$ then inverse of f is equal to

The Attempt at a Solution

The two possibilities are
$exp (\dfrac{-3\pm\sqrt{4x+1}}{2})$

How to decide which one is correct?

 

[Saitama]

Homework Statement

Let f be a function defined as f:(0,exp-3/2) → [-1/4, ∞),
$f(x) = (ln x)^2 + 3 ln x + 2$ then inverse of f is equal to

The Attempt at a Solution

The two possibilities are
$exp (\dfrac{-3\pm\sqrt{4x+1}}{2})$

How to decide which one is correct?

Try plugging $x=2$ in the inverse function. That should help you in figuring out the correct sign.

 

[LCKurtz]

Or note that one of your choices is always negative.