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

Question

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.

Answer 1

your answer is correct.

for the restriction, the denominator cannot be zero, so x≠1
also the inside of the square root cannot be negative,
this will happen when -1 ≤ x ≤ +1

so the domain is x ≤ -1 OR x > 1
as x gets +large, the expression approaches 1
as x gets -large, the expression approaches -1
range: y >1 OR y < -1