What is the domain of the function f(x)= x + 1 / x^2 - 6x + 8?PLEASE ANSWER FAST IM TIMEDall real numbersall real numbers except –1all real numbers except –4 and –2all real numbers except 2 and 4
Accepted Solution
A:
Answer: all real numbers except 4 and 2
Explanation: The given function is: f(x) = [tex] \frac{x+1}{x^2-6x+8} [/tex]
Domain of the function is defined as the values of x that can be used to substitute in the function.
We know that any fraction cannot have a zero in its denominator. Because if this happens, then the fraction would be undefined.
This means that in the given function, we cannot substitute with any value for x that makes the denominator a zero.
Now, we will get the zeroes of the denominator as follows: x² - 6x + 8 = 0 (x-4)(x-2) = 0 either x-4 = 0 ...........> x = 4 or x-2 = 0 .............> x = 2
Based on the above, we can substitute with any value for x excluding 4 and 2.
This means that the domain of the function is any real real number except 4 and 2