Let f(a) √x-4 and g(x)=x+6 What are f+g and f-g? What are their domains?

Answer 1

When we add functions, we simply add them:

f(x) = √x- 4

g(x) = x + 6

f(x) + g(x) = (√x- 4)+(x+ 6)

f(x) - g(x) = (√x- 4)-(x+ 6)

We know the definition of the domain is "all x values for which there is a corresponding y value," so we aim to understand for what values of x the function is defined. We know that we cannot have a negative number under the square root, so we use the below function to understand what value(s) of x would make that happen:

(x-4) ≥ 0

x ≥ 4

So, we know that the domain of these functions is x ≥ 4 for both f(x) + g(x) and f(x) - g(x)