Question

Describe and correct the error a student made in finding the domain for the quotient when f(x) = 2x² - 3x + 1 and g(x) = 2x - 1.

So the domain is all real numbers.​

Answer 1

The student is correct that the domain of a quotient is typically all real numbers, except for the values of x that make the denominator equal to zero.

However, it's important to check whether the denominator of the quotient, g(x), can ever be zero. In this case, the denominator is 2x - 1. Setting this equal to zero, we get:

2x - 1 = 0
2x = 1
x = 1/2

Therefore, the only value of x that is not in the domain of the quotient is x = 1/2. The correct domain for the quotient is all real numbers except x = 1/2.

So the correct domain is:

x ≠ 1/2

It's important to double-check for such possible errors while finding the domain of a function.