Question

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

Answer 1

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{*}`.