# Thread: Inverse of a Function

1. ## 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

2. $\displaystyle f(x)= (x+1)^3$

$\displaystyle y = (x+1)^3$

Switch y and x:

$\displaystyle x = (y+1)^3$

Solve for y. Take the cube root both sides:

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

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

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.

3. 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

4. Consider this equation: $\displaystyle x^n = a$

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

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 $\displaystyle x = +\sqrt[n]{b}$. Otherwise, if b is negative, then $\displaystyle x = -\sqrt[n]{b}$