SOLUTION: For​ f(x) as​ given, write the domain of f. f(x)=x+8/2x−8 The domain of f is _____ ​(Type your answer in interval​ notation.) I think the answ

Algebra ->  Absolute-value -> SOLUTION: For​ f(x) as​ given, write the domain of f. f(x)=x+8/2x−8 The domain of f is _____ ​(Type your answer in interval​ notation.) I think the answ      Log On


   

Question 1111201: For​ f(x) as​ given, write the domain of f.
f(x)=x+8/2x−8
The domain of f is _____
​(Type your answer in interval​ notation.)
I think the answer is x=4 with a line through the equal sign, but how do I put that in interval notation?
Found 4 solutions by josgarithmetic, TeachMath, ikleyn, amalm06:
Answer by josgarithmetic(39627) About Me  (Show Source):
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?
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%28x%2B8%29%2F%282x-8%29

Numerator could be any real number as could be x but NOT the denominator.
Restriction is x%3C%3E4.

Domain?
The set of all real numbers which are less than 4 AND the set of real numbers greater than 4 are the domain for f.

Answer by TeachMath(96) About Me  (Show Source):
You can put this solution on YOUR website!
You are DEFINITELY correct that the domain is NOT EQUAL to 4, or, it's all reals, EXCEPT 4.

In INTERVAL NOTATION, this is: (- infinity, 4)U(4, infinity)
PAY no attention to any answer that's different!
The other person who said that x is not equal to 8 is WRONG, as usual.

Answer by ikleyn(52864) About Me  (Show Source):
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.
If f(x) = %28x%2B8%29%2F%282x-8%29,  then


the domain is the set of all real numbers except of x = 4.


In the interval notation,  the domain = (-infinity,4) U (4,infinity).


It is the same as to say that the domain is the entire number line with the hole at x= 4.

Next time, when you post formulas to the forum, use parentheses to point which part is the numerator and which is the denominator.


Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
Set the denominator equal to 0:
2x-8=0
2x=8
x=4
So the domain is the set of all real numbers, except for 4
In interval notation: x ∈ (-∞,4) U (4,∞) (Answer)