Question

Which of the following functions have only one point that is not in the domain? Select all that apply. (There are 2 answers)

Answer 1

Answer:

  B.  f(x) = 3/(x^2 +2x +1)

  E.  f(x) = 5/(3+x)

Step-by-step explanation:

The above functions have denominators that are zero at one point. For B, that point is x=-1; for E, that point is x=-3. When the denominator is zero, the function is undefined, so the corresponding x-value must be excluded from the domain.

__

As written, choice D also qualifies. This is because the function written in the answer list here is ...

$f(x)=\dfrac{1}{x^2}+5x+4$

It will be undefined for x=0.

_____

Comment on writing rational functions

When the division symbol (/ or ÷) is used with a denominator that is a product or sum, that product or sum must be enclosed in parentheses. When the expression is typeset, the division bar acts as a grouping symbol. When the expression is written in text, a grouping symbol, such as parentheses, must be added.