Question

What is the domain of the combined function `h(x) = f(x) - g(x)` , if the domain of f(x) = (4,4.5] and the domain of g(x) is [4, 4.5)?

Answer 1

The domain is `D_{f-g}=(4,4.5)`. See explanation.

Explanation:

`(f-g)(x)` can only be calculated for those `x`, for which both `f` and `g` are defined. So we can write that:

`D_{f-g}=D_fnnD_g`

Here we have `D_{f-g}=(4,4.5]nn[4,4.5)=(4,4.5)`