Draw the graph of `y=log_(e)(x^(2)-1)`

Explanation

`y = log_(e)(x^(2)-1)`
Domain of the function is `x^(2)-1 gt 0` or `x in (-infty,-1) cup (1,infty)`
For `x gt 1, x^(2)-1 gt 0`
`therefore log(e )(x^(2)-1)in (-infty, infty)`
Also `log_(e)(x^(2)-1)` increases as `x` increases.
Graph intercepts the x-axis if y=0 or `log_(e)(x^(2)-1)=0` or `x^(2)-1=1` or `x^(2)=2` or `x=x+-sqrt(2)`.