Define F(x)= cases x^ 2 -1 x-1 , & x<1 e^ x-1 , & 1 x<3 x , & x 3 cases Identify…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Define

F(x)=\begin{cases}\dfrac{x^{2}-1}{x-1}, & x<1\\ e^{x-1}, & 1\le x<3\\ \lfloor x\rfloor, & x\ge 3\end{cases}

Identify every

x

-value at which

F

is discontinuous on

(-\infty,\infty)

and classify each discontinuity as removable, jump, or infinite.