Question

How do you find the domain of f+g given f(x)=3x + 4 and g(x) = 5/(4-x)?

Answer 1

The domain of the sum of two functions is the intersection of their domains.

Explanation:

First of all, let us find the domain of `f(x)` and `g(x)` independently:

• `f(x)` is a polynomial function, so its domain is `RR`.
• `g(x)` is a fractional function, so its domain is `RR` excepting those points where the denominator vanishes:

`4-x = 0 rightarrow x = 4`

So the domain of `g(x)` is `RR - {4}`.

Now, the domain of

`(f+g)(x) = 3x+4 + 5/{4-x}`

consists of those points where both `f(x)` and `g(x)` exist, this is the intersection of both domains. Since both domains are `RR` except the second one, which excludes the value `x=4`, the domain of the sum is:

`"Dom" (f+g) (x) = RR - {4}`