Question

Explain why f(x) = x2+4/x2-x-2 is not continuous at x = 2.

Answer 1

Explanation:

We have given a function :

f(x) = (x²+4)/(x²-x-2)

We have to explain why the function is not continuous at x = 2.

Simplify the denominator of the function.

x²-x-2 = x²+x-2x-2

x²-x-2 = (x+1)(x-2)

Putting this simplification of denominator in above function we get,

f(x) = (x²+4)/(x+1)(x-2)

The domain is the all possible values of x in for which the function is defined.

when we put x=2, the denominator is zero and function is undifined.

So, the function is not continuous at x = 2.

Choice a is correct.

Answer 2

Answer: Option a.

Explanation:

Make the denominator equal to zero and solve for x:

Factor the quadratic equation. Find two number whose sum is -1 and whose product is -2. Then:

`x^(2)-x-2=0\\(x-2)(x+1)=0\\x=2\\x=-1`

Then, as you can see the value x=2 makes the denominator equal to zero and the division by zero does not exist. Therefore you can conclude that the function shown in the problem is not defined at x=2

The answer is the option a.