$f(x)=\left\{\begin{array}{cc} \frac{x-4}{|x-4|}+a, & ext { for } x 4 \end{array} ight.$ Is continuous at $x=4$, then

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$f(x)=\left\{\begin{array}{cc} \frac{x-4}{|x-4|}+a, & 	ext { for } x 4 \end{array}ight.$ Is continuous at $x=4$, then

Aicharya · Accepted Answer

For continuity at $x=4$ $\begin{aligned} & \lim _{x ightarrow 4^{-}} f(x)=f(4)=\lim _{x ightarrow 4^{+}} f(x) \ & \Rightarrow \lim _{x ightarrow 4^{-}} \frac{x-4}{|x-4|}+a=a+b=\lim _{x ightarrow 4^{+}} \frac{x-4}{|x-4|}+b \ & \Rightarrow-1+a=a+b=1+b \ & \Rightarrow a=1 	ext { and } b=-1 \end{aligned}$

$f(x)=\left\{\begin{array}{cc} \frac{x-4}{|x-4|}+a, & \text { for } x 4 \end{array}\right.$ Is continuous at…

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