How do you find the domain and range of #f(x)=1/(2x-4)#?

1 Answer
Apr 16, 2018

Answer:

The domain is #\mathbb{R} text{\} {2}# and the range is #\mathbb{R}^text{*}#.

Explanation:

We have:

#f(x)=1/(2x-4)#

The function is defined for all reals except for #2x=4# (#x=2#) because you can't divide by #0#. So the domain is #\mathbb{R} text{\} {2}#.

#f(x)# can take any real value except for #0#, as a fraction is equal to zero only if the numerator is also equal to #0#. Thus, the range is #\mathbb{R} text{\} {0}=\mathbb{R}^text{*}#.