43.1. Plot the graph of the function

$$
y=\sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}}
$$
43.1. It is easy to see that $x+2 \sqrt{x-1}=(1+\sqrt{x-1})^{2}$ and $x-2 \sqrt{x-1}=(1-\sqrt{x-1})^{2}$. It is obvious that the given function is defined for $x \geqslant 1$. Now it is not difficult to represent this function in the following form:

$$
y=\left\{\begin{array}{l}
2, \text { if } \quad 1 \leqslant x \leqslant 2 ; \\
2 \sqrt{x-1,} \text { if } x>2 .
\end{array}\right.
$$

The obtained expression for the function allows us to easily plot its graph (Fig. 10).

![](https://cdn.mathpix.com/cropped/2024_05_21_f0d089db3d527e92a992g-24.jpg?height=534&width=654&top_left_y=1395&top_left_x=701)

Fig. 10