For f(x)=(x-3)/(x^(2)-4), the function is at x=2 continuous discontinuous with an infinite discontinuity discontinuous with a jump discontinuity discontinuous with a point disco…

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asked Jun 20, 2021 135k views

2 Answers

AngelsandDemons · Answer 1 · 2021-06-23T11:03:04+0000

Answer:

$\Large \boxed{\mathrm{discontinuous \ with \ a \ point \ discontinuity}}$

$\rule[225]{225}{2}$

Explanation:

$\displaystyle f(x)=(x-3)/(x^2-4)$

When x = 2.

We can see that the denominator is equal to 0 when the input value is 2.

2^2-4=4-4=0

Obtaining a zero in the denominator indicates a point of discontinuity.

In the graph below, we can see that the function is discontinuous at x = 2.

$\rule[225]{225}{2}$