Hi
What will be the range of the function f(x) = 1-1/x .
1. The domain is given as [0, infinity)
2. The domain is given as [0, infinity]
I am primarily confused if "1" will be included or not? The limit of the function tends to 1 but it will never actually reach 1. So, will the range be [-infinity,1) or [-infinity,1] or (-infinity,1) or (-infinity,1]
thanks
hmm ok . (0,infinity) is because infinity cant be included in the set right? Its not any proper number.
@Prove It : I found the range. Its coming out to be -infinity to 1. But I am not sure if 1 is actually included or not because
Lim 1/x (x tends to infinity) ---> 0
so 1-1/x = 1-0 = 1
but
But 1/(some very large number ) ----> some very tiny number like 0.000000000045
So, 1-1/x = 1-some very tiny number. = 0.99999999999999434
SO, the range is (-infinity,1) or (-infinity,1] ?
Let's put it this way...
In the domain , (since as pointed out earlier), the range of the function is , or in interval notation, .
Notice that as . BUT since we can never reach , will never reach .
Now the reflection in the axis means that the range of becomes , or to use interval notation, .
The translation of 1 unit vertically upward means that the range of is , or in interval notation.
So to answer your question, you do NOT include the 1 in the range.