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)
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.
To find the common domain of h(x) = f(x) + g(x), we need to consider the domains of both f(x) and g(x) and find the overlapping region.
For f(x) = x^2 - 1, the domain is given as -2 ≤ x < 4. This means that x can take any value between -2 (inclusive) and 4 (exclusive).
For g(x) = 2/x - 3, the domain is given as 0 < x ≤ 5. This means that x can take any value between 0 (exclusive) and 5 (inclusive).
To find the common domain, we need to determine the overlapping region between -2 ≤ x < 4 and 0 < x ≤ 5.
The overlapping region is 0 < x < 4, as x cannot take values that are equal to either -2 or 4.
Therefore, the common domain of h(x) = f(x) + g(x) is 0 < x < 4.