How do you find the inverse of #f(x) = x^3 + 5# and is it a function?

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Answer 1 · 2018-07-28T12:48:51

#f^-1(x) = root (3) (x-5)#, yes it is a function.

#f(x) = x^3+5# or

#y = x^3+5# or

#x = y^3+5# [switch #x and y# and solve for y]

#y^3= x-5 or y = root (3) (x-5)# or

#f^-1(x) = root (3) (x-5)#

Since in the equation one #x# yield exactly one #y#, then

it is a function.

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