Answer:
f is not defined at x = 3
Explanation:
In any fraction, the denominator cannot be zero. This is because, a fraction would be undefined if its denominator is equal to zero.
Now, for the given function, we have the denominator:
x² - 9
This denominator cannot be zero. To get the value of x that would would make the function undefined, we would need to factorize the denominator as follows:
x² - 9 = 0
(x+3)(x-3) = 0
This means that:
either x-3 = 0 ...........> x = 3
or x+3 = 0 .........> x = -3
This means that our function is undefined at x = 3 and at x = -3, which also means that the function is discontinuous at these two values.
Since the question is asking specifically about the value x = 3, therefore, our answer should be related to the same value (x=3). Therefore, we would choose option b and not option a.
Hope this helps :)
