# How do you find the domain and range of f(x)=1/(x+3)?

Jul 4, 2016

${D}_{f} = \mathbb{R} - \left\{- 3\right\} .$
${R}_{f} = \mathbb{R} - \left\{0\right\} .$

#### Explanation:

Remember that Division by $0$ is not allowed, so, in our $f \left(x\right) , x + 3 \ne 0. i . e . , x \ne - 3$.

So, Domain of $f$, denoted by ${D}_{f}$, is $\mathbb{R} - \left\{- 3\right\} .$

Also, note that, $\forall x \in {D}_{f}$, $f \left(x\right) \ne 0$, if so, then $\frac{1}{x + 3} = 0 \Rightarrow 1 = 0$, an impossibility. That gives us the Range of $f = {R}_{f} = \mathbb{R} - \left\{0\right\} .$