Answer:
[tex]\{x\in R\ |\ x\ne 2 \}[/tex]
Step-by-step explanation:
The domain of a function is the set of x-values for which the function produces a real output (y-value).
By default, polynomials have a domain of:
[tex]x\in R[/tex]
or All Real Numbers.
We are given a rational function, which may have undefined points if the numerator and denominator are both zero at some x-values.
We can find these by factoring:
[tex]f(x) = \dfrac{x^2-x-2}{x^2-5x+6}[/tex]
[tex]f(x) = \dfrac{(x-2)(x+1)}{(x-2)(x-3)}[/tex]
Since x - 2 = 0 when x = -2, the function is undefined at that point. Therefore, this function's domain is:
[tex]\{x\in R\ |\ x\ne 2 \}[/tex]
When x = 2:
[tex]f(2) = \dfrac{(2-2)(2+1)}{(2-2)(2-3)} = \textsf{''}\dfrac{0}{0}\textsf{''}[/tex]
