Question

How do you find the domain and range of `1/(x+1)`?

Answer 1

Domain: `(-oo, -1) uu (-1, +oo)`
Range: `(-oo, 0) uu (0, +oo)`

Explanation:

The domain of the function will have to take into account the fact that the denominator of the fraction cannot be equal to zero.

This means that any value of `x` that makes the expression `x+1=0` will be excluded from the domain.

More specifically, you have

`x+1 = 0 => x = -1`

The domain of the function will thus be `RR-{-1}`, or `(-oo, -1) uu (-1, +oo)`.

The range of the function will be influenced by the fact that you don't have a value of `x` for which the function is equal to zero.

The range of the function will thus be `RR-{0}`, or `(-oo, 0) uu (0, +oo)`.

graph{1/(x+1) [-10, 10, -5, 5]}