2.7.49 Function properties

Condition: The function \( y=f(x) \) and two argument values ​​\( x_{1} \) and \( x_{2} \) are given. It is required to establish whether a given function is continuous or discontinuous for each of the given argument values: in the case of a discontinuity, find the limits at the discontinuity point on the right and left and make a schematic drawing of the function near the discontinuity point. \[ f(x)=e^{\frac{1}{1-x}}, \quad x_{1}=1, \quad x_{2}=5 \text {. } \]