# Inverse of a Function

• Aug 17th 2008, 05:01 PM
falloutatthedisco
Inverse of a Function
Would the inverse of

f(x)= (x+1)^3

be

y = + (the square root of x) - 1

or

y= y = - (the square root of x) - 1

thanks
• Aug 17th 2008, 05:06 PM
Chop Suey
$f(x)= (x+1)^3$

$y = (x+1)^3$

Switch y and x:

$x = (y+1)^3$

Solve for y. Take the cube root both sides:

$\sqrt[3]{x} = y+1$

$y = \sqrt[3]{x} - 1$

It's neither. If you made a mistake and you actually meant cube root of x instead of square root of x, then the first one is the one.
• Aug 17th 2008, 05:22 PM
falloutatthedisco
I did mean the cube root, I'm sorry. I was talking on the phone to my friend about a different problem, ironically, so I messed up. so there's no +/-, it's only plus?

thanks
• Aug 17th 2008, 05:50 PM
Chop Suey
Consider this equation: $x^n = a$

Case 1:
If n is even and a>0, then there are two roots: $x = \pm\sqrt[n]{a}$

Case 2:
If n is odd, then there is one root, and it depends on whether a is positive or negative. If b is positive, then $x = +\sqrt[n]{b}$. Otherwise, if b is negative, then $x = -\sqrt[n]{b}$