Answer
$y$-intercepts: (0, 1) and (0, -1)
$x$-intercepts: $\left(\frac{\sqrt 3}{3}, 0\right)$ and $\left(-\frac{\sqrt 3}{3}, 0\right)$
Work Step by Step
To find the $y$-intercept(s), set $x=0$.
\begin{align*}
y&=2(0)-\sqrt(0^2+1) \\
&=0-\sqrt (1) \\
&=0-(\pm 1) \\
&=\pm 1
\end{align*}
Thus, the $y$-intercepts are (0, 1) and (0, -1).
To find the $x$-intercept(s), set $y=0$.
\begin{align*}
0&=2x-\sqrt(x^2+1) \\
\sqrt(x^2+1)&=2x \\
x^2+1&=4x^2 \\
1&=3x^2 \\
\frac{1}{3}&=x^2 \\
x&=\sqrt\frac{1}{3} \\
&=\frac{\sqrt 1}{\sqrt 3} \\
&=\frac{\pm 1}{\sqrt 3} \\
&=\frac{\pm 1}{\sqrt 3}\left(\frac{\sqrt 3}{\sqrt 3}\right) \\
&=\pm\frac{\sqrt 3}{3}
\end{align*}
Thus, the $x$-intercepts are $\left(\frac{\sqrt 3}{3}, 0\right)$ and $\left(-\frac{\sqrt 3}{3}, 0\right)$.
