Answer
$a.\quad x=0$ and $x=2.32$
$b.\quad x\in[2.32,\infty)$
Work Step by Step
$a.$
Graph $f(x)=1+\sqrt{x}$ (red on the image)
and $g(x)=\sqrt{x^{2}+1}$ (blue).
The solution (if it exists) is the x-coordinate of the intersection.
Solution: $x=0$ and $x=2.32$
$b.$
Using the graphs of part (a), we see that
the red graph is above but not intersecting the blue graph on
$[2.32,\infty)$
