Final answer:
The domain of the function (x-2)/(2x²+x-10) is all real numbers except for 5/2 and -2. The correct domain is option (A): (-∞,-5/2)∞,2)∞).
Step-by-step explanation:
The domain of a function is the set of all possible inputs (x-values) for which the function is defined. In the case of the function (x-2)/(2x²+x-10), we need to determine the values of x for which the function is not defined. This happens when the denominator is equal to zero since division by zero is undefined. The denominator 2x²+x-10 can be factored into (2x-5)(x+2). Setting the factors equal to zero gives us two values that x cannot be: x = 5/2 and x = -2.
To find the domain, we take all real numbers and subtract the values that are not allowed. The result is three intervals where the function is defined: (-∞,-5/2), (-5/2,2) and (2,∞). However, even though x = 2 is not restricted by the denominator, x = 2 makes the numerator zero which is allowed. Therefore, the number 2 is included in the domain. The correct answer is (A) (-∞,-5/2)∞,2)∞).