How do I find the domain in this problem? Is it that the denominator cannot equal zero still?
x^2-x/(x^2-x)+2
correct, just figure out which x makes the bottom zero.
I see two values.
would it be 0 and 1
correct
thank u
To find the domain of the given function, we need to determine the values of x for which the function is defined. The main concern is the denominator since dividing by zero is undefined.
The expression provided is:
(x^2 - x) / (x^2 - x + 2)
To find the domain, we need to consider the values of x that make the denominator equal to zero.
For the given denominator x^2 - x + 2, we can determine if it can equal zero by setting it equal to zero and solving for x:
x^2 - x + 2 = 0
The solutions to this equation represent the values of x that would make the denominator zero and, therefore, the function undefined.
Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 1, b = -1, and c = 2. Plugging these values into the quadratic formula:
x = (-(-1) ± √((-1)^2 - 4(1)(2))) / (2(1))
= (1 ± √(1 - 8)) / 2
= (1 ± √(-7)) / 2
Since the square root of a negative number is undefined in the real number system, there are no real values of x that would make the denominator zero.
Therefore, the domain of the given function is all real numbers, because the denominator can never equal zero.