SOLUTION: The function f is defined by f(x) = x^3
Find the expression for g(x) in terms of x in each of the following cases
(a) f(g(x)) = x + 1
(b) g(f(x)) = x + 1
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-> SOLUTION: The function f is defined by f(x) = x^3
Find the expression for g(x) in terms of x in each of the following cases
(a) f(g(x)) = x + 1
(b) g(f(x)) = x + 1
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Question 509370: The function f is defined by f(x) = x^3
Find the expression for g(x) in terms of x in each of the following cases
(a) f(g(x)) = x + 1
(b) g(f(x)) = x + 1 Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website! Interesting question.
Let's figure out what the INVERSE of f(x) is.
y = x^3
cbrt stands for cube root or 'third root'
cbrt(y) = x
Switch x and y
y = cbrt(x)
So if we were to put in cbrt(x) as our g(x), by definition f(g(x)) = x.
But we want x+1.
So we put in cbrt(x+1), and that is our answer for part a.
Again the inverse of f(x) is cbrt(x).
So cbrt(f(x)) = x
We want our end result to be x+1.
So g(x) must be cbrt(x) + 1. <--- Part b answer
