B2. a) Draw the graph of the function $f$ defined by

$$
f(x)=\left\{\begin{array}{rll}
2 x+1 & \text { for } & x>1 \\
-x+5 & \text { for } & x \leq 1
\end{array}\right.
$$

b) Let $g(x)=2 x+1$. Write all values of the variable $x$ for which the equation $g^{-1}(x)=g\left(x^{-1}\right)$ holds?

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-08.jpg?height=848&width=865&top_left_y=835&top_left_x=638)
B2.

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-22.jpg?height=846&width=857&top_left_y=288&top_left_x=611)
a) Correctly drawn line $z$ with the equation $y=2x+1$ or a part of this line ..... 1 point
Correctly drawn line $z$ with the equation $y=-x+5$ or a part of this line ..... 1 point
Correctly labeled graph of the function $f \mathbf{v} x=1$ ..... 1 point
b) Procedure for calculating the inverse function ..... $1^{*}$ point
Writing $g^{-1}(x)=\frac{x-1}{2}$ ..... 1 point
Writing $g\left(x^{-1}\right)=2 x^{-1}+1$ ..... 1 point
Writing the equation $x^{2}-3 x-4=0$ ..... 1 point
Writing the solutions of the equation $x_{1}=4$ and $x_{2}=-1$ ..... 1 point