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
$\displaystyle f(x)= (x+1)^3$
$\displaystyle y = (x+1)^3$
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.
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 $\displaystyle x = -\sqrt[n]{b}$