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

1 Answer
Jun 15, 2016

Answer:

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}#