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January 6th, 2015, 03:06 AM   #1
Joined: Oct 2013

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function composition

For each of the following functions g: R → R state how many functions f: R → R exist such that f(g(x)) = x^2.

(l) g(x) = x
(m) g(x) = x^2
(n) g(x) = (x − 1)^2

I was doing this question and I only got (n) right (and I understand this). The answers given are 1, an infinite number and none. What I don't get is why the answers for part (l) and (m) are 1 and infinite.
For example for part (l) aren't 2 acceptable functions for f(x)=x^2 and f(x)=|x|^2 and if not then what are some forms of the infinitely many functions for part (m)?

Last edited by skipjack; January 6th, 2015 at 04:06 AM.
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