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

1 Answer
Miguel F.
Jun 15, 2016

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}

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