the domain of the function f(x) = log[x] base to |x|
If the base is x, then all you need is x > 0
The graph is interesting. See
https://www.wolframalpha.com/input/?i=log_x%28floor%28x%29%29
Oops - my bad. Since [x]=0 for x<1, you need x > 1
To find the domain of a function, we need to consider the values of x for which the function is defined.
In the case of f(x) = log[x] base |x|, the base of the logarithm is |x|, which implies that x must be non-zero. This is because the logarithm of 0 is undefined.
However, we also need to consider the argument of the logarithm, which in this case is [x]. The expression [x] represents the greatest integer less than or equal to x. Since this function uses the greatest integer function, we have to ensure that the argument is greater than zero.
Combining these conditions, we can obtain the domain of the function:
1. The base of the logarithm, |x|, must be non-zero: |x| ≠ 0.
2. The argument of the logarithm, [x], must be greater than zero: [x] > 0.
By considering these conditions together, we conclude that the domain of the function f(x) = log[x] base |x| is all real numbers except 0.