SOLUTION: Determine the maximal domains of the functions f(x) = 1/x−5 and g(x) = √8-2x

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Question 1092458: Determine the maximal domains of the functions f(x) = 1/x−5
and g(x) =
√8-2x
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
For the function  f(x) = (1/x) - 5 the domain is the entire number line, except x= 0 where the denominator is zero.


For the function  f(x) = 1/(x - 5) the domain is the entire number line, except x= 5 where the denominator is zero.


For the function  f(x) = sqrt(8-2x)  the domain is the set  8-2x >= 0,   or, which is the same,

8 >= 2x,   or   x <= 4,

providing that the binomial under the square root is non-negative.


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Unfortunately, from your writing I can not distinguish which of the two fractions you are asking about,  (1/x) - 5  or  1/(x - 5).

In the future,  when you will post formulas to this forum,  use parentheses to make your formulas unambiguous.

Using parentheses in formulas is  THE RULE  and  THE REQUIREMENT  in this forum.

Thank you.