1. Tardigrade
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  4. If the function f(x) = begincases a | π - x | + 1 , x le 5 b | x - π | + 3 , x > 5 endcases is continuous at x = 5, then the value of a - b is :-

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Q. If the function $f(x) = \begin{cases} a | \pi - x | + 1 , x \le 5 \\ b | x - \pi | + 3 , x > 5 \end{cases} $ is continuous at x = 5, then the value of a - b is :-

JEE MainJEE Main 2019Continuity and Differentiability

Solution:

$a\left|\pi-5\right|+1 = b \left|5-\pi\right| +3$
$ a\left(5-\pi\right)+1 =b\left(5-\pi\right)+3 $
$ \left(a -b\right)\left(5-\pi\right) = 2 $
$ a-b = \frac{2}{5-\pi}$

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