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Domain & Range

F (x) = 2x+5

### 2 Answers by Expert Tutors

David F. | USNRC Training Professional – Mathematics TutorUSNRC Training Professional – Mathematic...
4.9 4.9 (96 lesson ratings) (96)
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Domain and range are basically asking "What are all of the possible values for  X (that's domain) and f(x) (that's range).  In some cases the domain is limited by things that aren't allowed mathematically, like dividing by zero.  If this were 1/(2X+5) it would be a totally different story.  In this case the domain would be restricted by the value of X=-5/2.  That value would make the denominator zero which is undefined.  With your example there are no restrictions to the value of X.  So the domain is All real values of X.

The range is simply asking "What are all of the possible values that the function can become?"  Again with your case we can find a value for X that would make the function become any value we choose.  So the range is "That f(X) can range from negative infinity to plus infinity.  Or again, the range would be all real values."  With range you have to again be aware of where the exception come in to play.  If I had a function that was simply x squared, f(X^2) then  we can see that no matter what X is equal to (positive or negative) once we square it, it becomes a positive number.  In this case the range would be all the real numbers from 0 on up to infinity, but not negative numbers or less than zero.

Hope this helped explain it more so than to just answer your question.
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
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Domain is the possible values that, independent variable can take.

f(x) = 2x + 5

X can take all the real values, if we make a table of content, for each value of X, F(x) can take a real value.
X=1  f(x) = 7 , x= 2  f(x) =9 , x = -3 f(x) = -1,......
Domain of f(x) = 2x +5     -infinity< X < + infinity

Range is all values that f(x) can take for values of X in domain

X = (f(x)- 5)/2)
f(x) = 7  x=1    f(x)= 9  X = 2  ,  f(x) =-1  x =-3
Range of f(x) = 2X+ 5   :    -infinity< x < + infinity.