domain of (12x+5)/(53)

Question

i am trying to find the domain of this problem and feel stupid

 

Answer 1

The domain is all values of x where you can plug in a value of x and get a valid answer from the function.  Consider the function 1/(x-2).  If I plug in x = 2, then I get 1/(2-2) = 1/0 which is undefined.  So x = 2 is not in the function's domain.  Any other value of x will produce a valid answer.  Another example is √(x). You can't take the square root of a negative number so the domain of √(x) is x≥0.

 

(12x+5)/53 is a linear function whose graph is a straight line stretching from -∞ to ∞.  There are no values of x where it is undefined.  Hence the domain is all x or (-∞, ∞).

Answer 2

Since there is no restriction on what x can be, the domain is all real numbers: (-∞,∞)

 

If x was in the denominator, there would be a restriction to keep the denominator from becoming zero.  If x was inside a square root, there would be a restriction to keep the argument of the square root from becoming negative.  But in this particular problem, there are no restrictions on x.

 

One more thing:  Never say you feel stupid.  That is self-defeating.  You can learn, and tutors are available to help.