State the domain of the quotient

Question

State the domain of the quotient f / g where f(x)=x-3 and g(x)=√x-1  Explain and show work 

Answer 1

State the domain of the quotient f / g where f(x)=x-3 and g(x)=√x-1

 

(f/g)(x) = (x-3)/(√(x) - 1)

 

Can't divide by zero:

 

√(x) - 1 ≠ 0

 

Add 1 to both sides:

 

√(x) ≠ 1

 

Square both sides:

 

x ≠ 1

 

So the domain of f/g is All Real Numbers Except 1.

 

In interval notation: x ∈ (–∞,1)U(1,∞)

Answer 2

By √x-1, we have x-1≥0, so x≥1. Since √x-1 is in the denominator, so x-1≠0, x≠1.

Therefore, x>1.