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Find the domain for the rational function f of x equals quantity x plus 4 over quantity 3 times x minus 5.
1. negative infinity to negative five thirds and negative five thirds to infinity
2. negative infinity to five thirds and five thirds to infinity
3. (−[infinity], −4)( −4, [infinity]) (−[infinity], 4)(4, [infinity])

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sqdancefan

Answer:

  2. negative infinity to five thirds and five thirds to infinity

Step-by-step explanation:

You want the domain of the rational function f(x) = (x +4)/(3x -5).

Domain

The domain is the set of input values for which the function is defined. A rational function is undefined when its denominator is zero. f(x) is undefined when ...

  3x -5 = 0

  x = 5/3

So, the value 5/3 must be excluded from the domain of f(x). The domain of f(x) is ...

  -∞ < x < 5/3  ∪  5/3 < x < ∞

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