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.

i need a picure

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.