Question

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])

Answer 1

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

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 < ∞