How do you find the inverse of #f(x) = x^3 + 4#?

Question

2634 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-02T15:33:50

The inverse of the function is #f^-1(x)=(x+4)^(1/3)#

Let #y=x^3+4#

Then

#x^3=y+4#

#=>#, #x=(y+4)^(1/3)#

Inverse the #y# and the #x#

#=>#, #y=(x+4)^(1/3)#

The inverse of the function is #f^-1(x)=(x+4)^(1/3)#

The inverse function is symmetric about the line #y=x#

And

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

graph{(y-x^3+4)(y-(x+4)^(1/3))(y-x)=0 [-10, 10, -5, 5]}