Question

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

Answer 1

We have `y= sqrt(x^(2) -1)`
or `" "y^(2) = x^(2)-1`
or `" "x^(2) -y^(2) =1`, which is a rectangular hyperbola.
But `" "y= sqrt (x^(2) -1) ge 0`
The graph of `y = f(x)` is part of the hyperbola `x^(2) - y^(2) =1`, which is lying above the x-axis.