With f(x) = x –3 and g (x) = √(x-2) What is the domain of the quotient function f/g.?

Question

With f(x) = x –3 and g (x) = √(x-2)
What is the domain of the quotient function f/g.

Answer 1

f(x) = x - 3

g(x) = √(x - 2)

(f/g)(x) = (x - 3)/√(x - 2)

This function is restricted by
1) The radical {since square roots are restricted to values greater than or equal to 0}
2) The rational {denominator can't equal 0}

What makes the denominator 0?

√(x - 2) = 0
x - 2 = 0
x = 2. Therefore, the domain will NOT include 2.

What makes the inside of the square root greater than or equal to 0?

x - 2 >= 0
x >= 2

Combine x >= 2 and x is not equal to 2, and we get

x > 2

The domain of this is the set of all x such that x > 2.

Answer 2

x-2>0 x in(2,∞)

Answer 3

The sqrt function g(x) must be greater than zero; therefore, the domain is x>2 or (2, +infinity).