How do you find the inverse of #f(x)=4x^7#?

1 Answer
Konstantinos Michailidis
Feb 28, 2017

Solve with respect to #x#

hence

#y=f(x)=4*x^7# hence

#x=(y/4)^(1/7)#

Replace #x# with #y# hence

#y=(x/4)^(1/7)#

or

#f^(-1) (x)=(x/4)^(1/7)#

To test that they are really inverses of each other you need to
find both composite functions #f(f^-1(x))# and #f^-1(f(x))#.
Both of these Must be equal to #x# or else they are not inverses of each other.

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