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

Answer 1

Abigail Allen

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

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

#4-x = 0 rightarrow x = 4#

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

As of right now, the realm 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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Answer 2

Nathan Axel

Domain of (f + g): All real numbers except x ≠ 4

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.