domain of a function

[@stevendebettencourt7651]

Things to watch out for that limit domains (assuming we are dealing with the Real Number system): -Division by zero -Even roots of negative numbers -Taking logarithms of 0 or less There may be other limitations I can’t recall right now, but those are the big three. If a value of x causes one of the above three situations, that value of x cannot be allowed. Let’s take the opening function: f(x) = 1/(x*sqrt(x-2)) First, we have to exclude any values of x that make us take the even root of a negative number. So: x-2 >= 0 x >= 2 But not so fast, my friend. Remember that we cannot divide by 0. So: x*sqrt(x-2) =/= 0 x =/= 0 AND sqrt(x-2) =/= 0 The value of x=0 was already excluded due to causing the square root of a negative number. But let’s follow the other road: Sqrt(x-2) =/= 0 x-2 =/= 0 x =/= 2 So the value x=2 is also excluded. So the whole domain of this function is all Real Numbers such that x > 2, or if you are a fan of set theory, you could show the domain as (2,infinity).

[@russelllomando8460]

nice lesson

[@terry_willis]

b)

[@robmartin5518]

minus 10 points from your grade.