B1. Write the domain of the function $f(x)=\sqrt{5-x^{2}}$.
B1. The core function is defined for $5-x^{2} \geq 0$. If we factorize $5-x^{2}$, we get $(\sqrt{5}-x)(\sqrt{5}+x) \geq 0$. From the graph, we can see for which values of the variable $x$ the function $y=5-x^{2}$ is non-negative: $[-\sqrt{5}, \sqrt{5}]$.

The graph of the function $f(x)=\sqrt{5-x^{2}}$ is drawn with a solid line, and the graph of the function $y=5-x^{2}$ is drawn with a dashed line.

Writing the condition $5-x^{2} \geq 0$ 1 point  
Factorization $(\sqrt{5}-x)(\sqrt{5}+x) \geq 0$ 1 point

![](https://cdn.mathpix.com/cropped/2024_06_07_8d4f73ada7862f989e67g-14.jpg?height=415&width=420&top_left_y=889&top_left_x=1495)

Zeros written: $x_{1}=\sqrt{5}$ 1 point

$x_{2}=-\sqrt{5}$

1 point

Appropriate sketch 1 point

Solution: $[-\sqrt{5}, \sqrt{5}]$ 1 point