Given f(x)= |x-1|/x^2-25 please determine the domain. Thank you!
A. All real numbers except -5 and 5
B. All real numbers except -5,0 and 5
C. All real numbers except 0
D. All real numbers except 0 and 5
the only thing you have to worry about in your function is division by zero
When does that happen?
When x^2 - 25 = 0
or when x^2 = 25
or when x = ± 5
so your domain is any real number, except x = ±5
which would be a)
Thank you for the explanation! My teacher really never explained it like you did. Do you teach math?
To determine the domain of the function, we need to identify any values of x that would make the function undefined. In this case, we have a rational function, where the denominator cannot be equal to zero.
The denominator of the function is x^2 - 25. So, we need to find the values of x that would make the denominator equal to zero, and exclude them from the domain.
To find these values, we set the denominator equal to zero and solve for x:
x^2 - 25 = 0
This is a quadratic equation, which can be factored as:
(x - 5)(x + 5) = 0
Setting each factor equal to zero, we get:
x - 5 = 0 --> x = 5
x + 5 = 0 --> x = -5
Therefore, the denominator is equal to zero when x equals -5 and x equals 5. These are the values that should be excluded from the domain.
So, the domain of the function f(x) = |x-1| / (x^2 - 25) is given by option A: All real numbers except -5 and 5.