# 5. Plot the graph of the function

$$
y=\frac{\sqrt{\frac{1+x^{2}}{2 x}+1}+\sqrt{\frac{1+x^{2}}{2 x}-1}}{\sqrt{\frac{1+x^{2}}{2 x}+1}-\sqrt{\frac{1+x^{2}}{2 x}-1}}
$$
Solution. $D(y)=\mathbf{R}_{+}$. After simplification, we get:

$$
y=\frac{1+x+|1-x|}{1+x-|1-x|}=\left\{\begin{array}{c}
\frac{1}{x}, \quad \text { for } 0<x<1 \\
x, \quad \text { for } x \geq 1
\end{array}\right.
$$

The graph of the function is shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_33455d0fbab9924c149ag-2.jpg?height=463&width=420&top_left_y=1990&top_left_x=721)