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

1 Answer
Apr 16, 2018

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{*}.