Which of the following functions have only one point that is not in the domain? select all that apply. (there are 2 answers)
a. f(x)=x^2-6x-8
b. f(x)=3/x^2+2x+1
c. f(x)=sqrt 2x-1
d. f(x)=1/x^2+5x+4
e. f(x)=5/3+x

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The domain of a function are the values that the input can assume, in this case, the possible values of x.

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Item a:

It is a simple quadratic function, with no impediments, so the domain is all real numbers, that is, there are no points that are not in the domain.

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Item b:

It is a fraction, so the impediment is that the denominator cannot be zero.

The denominator is , and it can be factored as a perfect square trinomial:

It is zero when:

Thus, it has only one point, x = -1, that is not in the domain.

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Item c:

The square root only exists for non-negative values, thus, the domain is:

Thus, there are infinite values not in the domain.

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Item d:

Another fraction, and the denominator can be factored as:

Which is zero at:

Thus, it has two points, x = -4 and x = -1, not in the domain.

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Item e:

Fraction, the denominator cannot be 0. So

There is one point, x = -3, not in the domain.

Thus, options B and E are selected.

A similar question is given at link

  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.

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

It will be undefined for x=0.

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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.