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

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- Aug 17th 2008, 04:01 PMfalloutatthediscoInverse 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, 04:06 PMChop Suey
$\displaystyle f(x)= (x+1)^3$

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

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. - Aug 17th 2008, 04:22 PMfalloutatthedisco
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, 04:50 PMChop Suey
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 $\displaystyle x = -\sqrt[n]{b}$