Question 77043: Find the numbers excluded from the domain.
a.) -2, 4/3 B.) 2, -4/3 c.) -2, 3/4 d.) 2, -3/4 Found 2 solutions by chitra, bucky:Answer by chitra(359) (Show Source):
To find the domain of the given function, we first factorize the denominator.
Here the denominator is
We find the roots of the above equation, either by factorization or by using the quadratic formula. The above expression cannot be solved by the factoring. so we use the quadratic formula, which is given by:
or
x = 2 or
These are the 2 numbers which are to be excluded from the set of domain. These numbers show that when plugged into the denomiantor gives us a zero. That is these two numbers are the roots of the polynomial in the denomiantor. Hence, they must be excluded from the domain.
Hence, the solution.
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Factor the denominator on the right side. You will have to play with this a while, but
without going into the process of factoring, I'll tell you that the denominator factors into
.
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Substitute this as the denominator in the original equation and you get:
.
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Now recognize that the rules of algebra do not allow dividing by zero. Therefore, neither
of the factors in the denominator can equal zero, because if either did equal zero, the
denominator would be zero.
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So you are not allowed to have . Solve for x by adding 2 to both sides of
this equation and you get x = +2. So you cannot allow x to equal +2.
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Next, the factor also cannot equal zero. So you are not allowed to have:
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Subtract 3 from both sides and this reduces to:
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Then solve for x by dividing both sides by 4 to get:
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So we cannot have x equal either. So the two value that x cannot be are +2 and
-3/4.
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Answer D is the correct choice.
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Hope this helps you to understand that division by zero is one of the things to look for
when you have an x term in the denominator because x cannot take any value that will cause
a division by zero.
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