ANSWER: The domain of given function is (-∞, -1) U (1, 3) U (3, ∞)SOLUTION:
Given, function [tex]f(x)=\frac{2 x-1}{(x-3)(x+1)}[/tex]We need to find the domain of the given function.
Domain is the set of numbers for which the function can be defined.
So, now let us find the set of numbers for which function becomes undefined, later we can remove from the universal set to get domain set.
Now, f(x) becomes undefined when, (x-3)(x+1) = 0 [since, anything divided by 0 is undefined]
(x - 3)= 0 or (x+1) = 0
x = 3 or -1
So, the function becomes undefined when x value is 3 or -1.
Now, let us remove the above values from universal set.
Then, the remaining set = (-∞, -1) U (1, 3) U (3, ∞).
Hence, the domain of given function is (-∞, -1) U (1, 3) U (3, ∞).