SOLUTION: Use the property of Inverse Functions to show that f and g are inverses of each other: f(x) = x^3 + 1; g(x) = (x-1)^(1/3) f(g(x)) = f((x-1)^1/3) + 1 = x-1 + 1 = x g(f(x)) =

Algebra ->  Algebra  -> Functions -> SOLUTION: Use the property of Inverse Functions to show that f and g are inverses of each other: f(x) = x^3 + 1; g(x) = (x-1)^(1/3) f(g(x)) = f((x-1)^1/3) + 1 = x-1 + 1 = x g(f(x)) =       Log On

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Question 45520This question is from textbook College Algebra
: Use the property of Inverse Functions to show that f and g are inverses of each other:
f(x) = x^3 + 1; g(x) = (x-1)^(1/3)
f(g(x)) = f((x-1)^1/3) + 1 = x-1 + 1 = x
g(f(x)) = g(x^3 + 1) = (x^3 + 1)^3 + 1 = x + 1 -1 = x
f and g are inverses of each other.
Thank you very much!This question is from textbook College Algebra

Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3 + 1; g(x) = (x-1)^(1/3)
f(g(x)) = f((x-1)^1/3)^3 + 1 = x-1 + 1 = x
g(f(x)=g(x^3 + 1) = [(x^3+1-1)^(1/3)]=[x^3]^(1/3) = x
Your conclusion is correct but I have adjusted your
posting.
Cheers,
Stan H.