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Explain why f(x) = x^2+4x+3/x^2-x-2 is not continuous at x = -1.

User Kareme
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1 Answer

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Answer:

The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)

Explanation:

We have the following expression


f(x) = (x^2+4x+3)/(x^2-x-2)

Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.

Now we search that values of x make 0 the denominator factoring the polynomial
x^2-x-2

We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.

These numbers are -2 and 1

Then the factors are:


(x-2) (x + 1)

We do the same with the numerator


x^2+4x+3

We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.

These numbers are 3 and 1

Then the factors are:


(x+3)(x + 1)

Therefore


f(x) = ((x+3)(x+1))/((x-2)(x+1))

Note that
((x+1))/((x+1))=1 only if
x \\eq -1

So since
x = -1 is not included in the domain the function has a discontinuity in
x = -1

User Rudy Seidinger
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7.5k points