Explain why f(x) = x^2-x-6/x^2-9 is continuous at x = 2.
a. f is defined at x = 3
b. f is not defined at x = 2
c. f is defined at x = -3
d. f is defined at x = 2
Answers
The correct answer is option D. ([tex]f[/tex] is defined at [tex]x = 2[/tex])
The rational Function is continuous at a given value if its Denominator is not zero. In this exercise, we proceed to Factor the expression by check the value Denominator for each value of [tex]x[/tex].
[tex]f(x) = \frac{x^{2}-x-6}{x^{2}-9}[/tex]
[tex]f(x) = \frac{(x-3)\cdot (x+2)}{(x+3)\cdot (x-3)}[/tex]
As we can see, [tex]f[/tex] is not defined for [tex]x = -3[/tex] and [tex]x = 3[/tex]. Hence, we conclude that right answer is D.
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This is my first solution, let me know if I can improve on anything. Thanks, have a great day!