How do you find the inverse of y=x4?

1 Answer
Dec 9, 2015

x=y2+4
or if you wish to keep y as the dependent variable:
y=x2+4

Explanation:

Method 1:
y=x4

y2=x4

y2+4=xXXxorXXXx=y2+4

Method 2: (perhaps more complex but more technically accurate)
Let
XXXf(x)=y
and
XXX¯¯¯¯¯¯¯f(x) be the inverse of f(x)

By definition of inverse:
XXXf(¯¯¯¯¯¯¯f(x))=x

But since
XXXf(x)=x4

XXXf(¯¯¯¯¯¯¯f(x))=¯¯¯¯¯¯¯f(x)4

So
XXX¯¯¯¯¯¯¯f(x)4=x

XXX¯¯¯¯¯¯¯f(x)4=x2

XXX¯¯¯¯¯¯¯f(x)=x2+4