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Need help with composition of functions

pcharles93

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pcharles93
OK, so I had this problem on a test last week and I haven't gotten it back yet so it's been really bugging me for a few days now.

If f(x)=sqrt(x-1) and g(x)=2-x^2, what is the domain of f(g(x))?

I figured that only 1 would work and was wondering if I was right.
 

ManasijV

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ManasijV
f(x)=sqrt(x-1) and g(x)=2-x^2
Therefore f(g(x))=sqrt(2-x^2-1)
=sqrt(1-x^2) ....... (What makes you think only one works?)
You know that square root of a negative number is imaginary.
So 1-x^2 > 0
ie x^2<1
ie -1<=x<=1
Thats the domain
Range is 0<=y<=1
 

pcharles93

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I guess I was trying to satisfy the domain of f(x) too. I see now that the range of g(x) has to be the domain of f(x). For g(x) >= 1, x^2 <= 1. So, the domain is [-1,1]. Well, I got half the domain right. I hope it was only worth 1 point on the test.
 
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