The function $f(x)=\left\{\begin{array}{ll}\frac{2}{5-x}, & x \lt 3 \ 5-x, & x \geq 3\end{array} ight.$ is

Question

The function $f(x)=\left\{\begin{array}{ll}\frac{2}{5-x}, & x \lt 3 \ 5-x, & x \geq 3\end{array}ight.$ is

Aicharya · Accepted Answer

Given, $f(x)= \begin{cases}\frac{2}{5-x}, & x \lt 3 \ 5-x, & x \geq 3\end{cases}$ $\begin{aligned} & \because \lim _{x ightarrow 3^{-}} f(x)=\lim _{x ightarrow 3^{-}} \frac{2}{5-x}=\frac{2}{5-3}=1 \ & \ & \lim _{x ightarrow 3^{+}} f(x)=\lim _{x ightarrow 3^{+}}(5-x)=2 	ext { and } f(3)=5-3=2 \end{aligned}$ Since, $\lim _{x ightarrow 3^{-}} f(x) 
eq \lim _{x ightarrow 3^{+}} f(x)=f(3)$ So, $f(x)$ is left discontinuous at $x=3$.

The function $f(x)=\left\{\begin{array}{ll}\frac{2}{5-x}, & x \lt 3 \\ 5-x, & x \geq 3\end{array}\right.$ is

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