Question 110
a) Draw the graph of the function $f$ given by
$$
f(x)=\begin{cases}
2x+1 & \text{for } x\gt 1 \\
-x+5 & \text{for } x \leq 1
\end{cases}
$$
b) Let $g(x)=2x+1$. Write down all values of the variable $x$ for which the equality $g^{-1}(x)=g\left(x^{-1}\right)$ holds.
$$
f(x)=\begin{cases}
2x+1 & \text{for } x\gt 1 \\
-x+5 & \text{for } x \leq 1
\end{cases}
$$
b) Let $g(x)=2x+1$. Write down all values of the variable $x$ for which the equality $g^{-1}(x)=g\left(x^{-1}\right)$ holds.