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

Apr 16, 2018

The domain is $\setminus m a t h \boldsymbol{R} \textrm{\setminus} \left\{2\right\}$ and the range is $\setminus m a t h {\boldsymbol{R}}^{\textrm{\cdot}}$.

#### Explanation:

We have:

$f \left(x\right) = \frac{1}{2 x - 4}$

The function is defined for all reals except for $2 x = 4$ ($x = 2$) because you can't divide by $0$. So the domain is $\setminus m a t h \boldsymbol{R} \textrm{\setminus} \left\{2\right\}$.

$f \left(x\right)$ 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 $\setminus m a t h \boldsymbol{R} \textrm{\setminus} \left\{0\right\} = \setminus m a t h {\boldsymbol{R}}^{\textrm{\cdot}}$.