What is the inverse of the function #g(x)=root5 (4x+2)#?

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Answer 1 · 2017-01-20T05:30:50

#x =1/4(g^5-2)#

graph{(x-1/4(y^5-2))=0 [-10, 10, -5, 5]} Adhering to the mathematical definition of inverse of a function;

#g^(-1)g(x)=x#

Here,

#g = (4x+2)^(1/5)#, giving

#4x+2=g^5#, and solving for x,

#x =1/4(g^5-2)#

Cross check :

The graphs of the function and the inverse have to be the same, for

locally bijective functions.

The two graphs appear separately, for identification

graph{(4x+2)^(1/5) [-10, 10, -5, 5]}