# Need help with composition of functions

#### pcharles93

##### Member
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.

#### fanwuq

##### Member
absolute value of x is less than or equal to 1.

#### pcharles93

##### Member
I see it now. We use interval notation for domain and range so I'm hoping my teacher misread part of a bracket as a negative sign.

#### ManasijV

##### Member
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

##### Member
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.