Posted by **Ed** on Thursday, September 23, 2010 at 3:09pm.

Find the quotient function f/g for f(x)=sqr(x+1) and g(x)= sqr( x-1).

My Answer:

sqr(x+1)/sqr( x-1)

sqr(x^2-1)/ (x-1)

However, I also have to state the restrictions to the domain and range, which I do not know how to do. Could someone please help me? Thanks.

- Math -
**MathMate**, Thursday, September 23, 2010 at 5:26pm
If Dom(f(x))=domain of f(x), and

Dom(g(x))=domain of g(x), the domain of f(x)/g(x) is the intersection

Dom(f(x))∩Dom(g(x))

However,by the definition of the quotient function, g(x) ≠ 0, therefore, we have to remove the members where g(x)=0 to get the final version:

Dom(f(x)/g(x))

= Dom(f(x))∩Dom(g(x)-{x:g(x)=0}

Note that:

Dom(√(x+1))

= [-1,∞]

Dom(√(x-1))

= [1,∞]

So

Dom(f(x)∩g(x))=[1,∞]

g(x)=0 when x=1, this has to be removed.

Therefore

Dom(f(x)/g(x))

=(1,∞)

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