For which value of x is undefined?

'Undefined' is usually another name for 'infinity', which always pops up when you try to divide by zero.
In this one, there's a fraction, and you're asked: "When is the fraction undefined ?"
If the denominator of the fraction is ever zero, then that's nothing but the old "division by zero", which is forbidden, not permitted, and undefined.
The denominator of the fraction is x² + 3x + 2 . Can that ever be zero ? It might be easier to see if you factor it: (x + 2) · (x + 1) = 0 This equation is true if x=-2 OR x=-1 . Either way, the denominator of the fraction is zero. So those are the values of 'x' for which the fraction is undefined.

Answered by AL2006 | 2024-06-10

The function is undefined for values of x that make the denominator equal to zero. In this case, for the expression x 2 + 3 x + 2 , the function is undefined at x = − 1 and x = − 2 . Always check the denominator of a fraction to identify points of undefined values in functions.
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Answered by AL2006 | 2024-12-23