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

Explanation

We have `y=f(x) = sqrt(1-x^(2))-x`
Clearly, the domain of function is R.
`f(0)=1`
`f(x)=0 therefore 1+x^(2)=x^(2)`, which is not possible.
Therefore, the function never intersect the x-axis.
Also, `sqrt(1+x^(2)) gt x, AA x in R`
graph of `y=f(x)` always lies above the x-axis.
`lim_(x to infty)(sqrt(1+x^(2))-x)=lim_(x to infty) 1/(sqrt(1+x^(2))+x)=0`
`lim_(x to infty) (sqrt(1+x^(2))-x)=infty`
`f^(')(x) = 1/sqrt(1+x^(2))-1=(1-sqrt(1+x^(2))/sqrt(1+x^(2)) lt 0), AA x in R`
Hence, the function is always decreasing.
From the above information, the graph of the function is as shown in the figure.