January 6th, 2015, 03:06 AM  #1 
Member Joined: Oct 2013 Posts: 36 Thanks: 0  function composition
For each of the following functions g: R â†’ R state how many functions f: R â†’ R exist such that f(g(x)) = x^2. (l) g(x) = x (m) g(x) = x^2 (n) g(x) = (x âˆ’ 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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composition, compostion, function 
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