Question #bbfbd

1 Answer
Aug 1, 2016

Answer:

Domain: #x in RR "\" {1}#

Range: #f(x) in RR "\" {0}#

Explanation:

I'm assuming that your function looks like this

#f(x) = 2/(x-1)#

The domain of the function includes any value of #x# for which #f(x)# is defined. This implies that the domain of the function will not include values of #x# for which the denominator is equal to zero.

In your case, you have

#x-1 !=0 implies x !=1#

Therefore, you can say that the domain of the function will include any value of #x in RR# with the exception of #x=1#, since that value would cause

#f(1) = 2/(1-1) = 2/0 -> # undefined

The domain will thus be #x in RR "\" {1}#.

The range of the function includes any value of #f(x)# that can be produced by plugging in the accepted values of #x#. Notice that in your case, you have no way of getting

#f(x) = 0#

That is the case because a fraction can only be equal to zero if its numerator is equal to zero.

Here the numerator of the fraction is equal to #2# regardless of the value of #x#. The range of the function will thus be #f(x) in RR "\" {0}#.

graph{2/(x-1) [-10, 10, -5, 5]}

You can use the exact same approach for the function

#f(x) = 2/x - 1#

This time, the value of #x# excluded from the domain will not be #x=1#, it will be #x=0#, since

#f(0) = 2/0 - 1 -># undefined

The range of the function will include #f(x) = 0#, but it will no longer include #f(x) = -1#

graph{2/x - 1 [-10, 10, -5, 5]}