if f(x)= 2 - x^1/2 and g(x)= x^2 - 9 , what is the domain of g(x)divided by f(x)

Question

Please help if you can!

Answer 1

For the numerator (x² - 9) there are no restrictions on "x" so the domain of that portion is all real numbers.

For the denominator, there are two issues. 1) because of the √x, x must be a number zero or larger since square roots of negative numbers are not real. and 2) because dividing by zero is not defined, 2 - √x must not equal zero or x ≠ 4

So the domain is the set of all numbers greater than or equal to zero but less than 4 combined with numbers greater than 4.

You can write that as an inequality: 0≤x<4 U 4<x<∞ or in interval notation as [0, 4) U (4, ∞)