Using operations on functions and determining domain

Question

The functions f(x)=x² and g(x)=√(x-3) are given, I found the domains of the functions to be (-∞,∞) and [1,∞) respectively. How do I find the domains of f+g, f-g, or fg? 

Answer 1

Lets focus on the function g(x).  g(x) is a special function because it has restrictions, unlike f(x).  The domain of x² is all real numbers.

 

Because g(x) is a square-root function, we can only have positive numbers including zero under this square-root.

 

Set the inequality to solve for x.

 

x - 3 ≥ 0

 

x ≥ 3

 

 

So the domain to all the combination of functions is all real number greater than or equal to 3.

Answer 2

For the function f + g, f - g, f.g, the domains are defined as the intersection of the domains of f and g.

 

When combining the 2 function, we should choose the domain that satisfies both the function - which is the intersection of the 2 domains.