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State the domain of the quotient

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2 Answers

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,∞)
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.