Question

Find the domain of this function ? Steps please

Answer 1

Domain: `(-1, oo)`

Explanation:

`f(x) = log_2 (x+1)`

It maybe easier to understand if we change the base to `log_e`

`f(x) = ln(x+1)/ln2`

Now, we know that `lnx` is defined for all `x>0` and since `ln2` is a constant it takes no part in this analysis.

`:. f(x)` is defined for all `(x+1)>0 -> x > -1`

Hence, the domain of `f(x)` is `(-1,oo)`

We can deduce this from the graph of `f(x)` below.

graph{ln(x+1)/ln2 [-10, 10, -5, 5]}