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asked • 12/26/12The function is defined below. h(x)=x-6/x^2-81
The function g is defined below. g(x)=(x^2)(-12x+35)/(x-5)
Find all values of
that are NOT in the domain of .
If there is more than one value, separate them with
commas.
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2 Answers By Expert Tutors
Inactive Tutor answered • 12/27/12
Tutor
New to Wyzant
for h(x)=(x-6)/(x2-81), any number devided by zero is undefined.
So equating you denominator to "0" and solve for x will gives values not in the domain.
→x2-81= x2-92=0 (difference of squares)
→(x-9)(x+9)=0
→x-9=0 and x+9=0
→x=9 and x=-9 not in the domain.
For the second question.
Again, the denominator is, x-5
→x-5=0
→x=5 is not in the domain.
Inactive Tutor answered • 12/26/12
Tutor
New to Wyzant
If I understand correctly, you are looking for values of x that are not in the domain of the function:
g(x)=(x^2)(-12x+35)/(x-5)
The key to finding values that are not in the domain of the function is finding any values that produce 0 in the denominator or negative numbers under radicals that have an even index (like a square root).
Since the function is a fraction, the domain of the function excludes any values of x that will cause the denominator to equal 0. To find these values, set the denominator equal to 0 and solve for x.
x - 5 = 0
x = 5
The value of x that is not in the domain of the function is x = 5.
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Inactive Tutor
What are you asking about the function? Are you asking for the domain? Do you need to find the 0's? Is there something else you need to know?
Also, is the function h(x)=x - (6/x2) -81 or is it h(x)=(x-6)/(x2-81)?
12/26/12