Question

What is the domain of the function y= 2/(x-5)?

a) x ≠ 5
b) x ≠ 2.5
c) x ≠ 0
d) x ≠ 5 and x ≠ 10

Answer 1

The domain of the function y = 2/(x-5) is all real numbers except x = 5, as this would result in division by zero.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. Looking at the function y = 2/(x-5), we must consider where the denominator equals zero, as this would create a division by zero, which is undefined. The denominator, x-5, is zero when x = 5. Therefore, the only value not in the domain is 5. So, the correct answer is a) x ≠ 5, meaning the function is defined for all x-values except x equals 5.