If f(x)=x^2-1,-2≤x<4 and g(x)=2/x-3, 0<x≤5. Find the common domain of h(x)=f(x)+g(x)

1 answer

To find the common domain of h(x) = f(x) + g(x), we need to find the intersection of the domains of f(x) and g(x).

For f(x), the given domain is -2 ≤ x < 4.
For g(x), the given domain is 0 < x ≤ 5.

To find the intersection of these two domains, we look for the common region between them. The overlap between -2 ≤ x < 4 and 0 < x ≤ 5 is the interval from 0 to 4:

0 < x < 4.

Therefore, the common domain of h(x) = f(x) + g(x) is 0 < x < 4.