Question:
If the function
$f(x)=\left\{\begin{array}{l}a|\pi-x|+1, x \leq 5 \\ b|x-\pi|+3, x>5\end{array}\right.$
is continuous at $x=5$, then the value of $a-b$ is:
Correct Option: , 4
Solution:
R.H.L. $\lim _{x \rightarrow 5^{+}} b|(x-\pi)|+3=(5-\pi) b+3$
$f(5)=$ L.H.L. $\lim _{x \rightarrow 5^{-}} a|(\pi-x)|+1=a(5-\pi)+1$
$\because$ function is continuous at $x=5$
$\therefore \mathrm{LHL}=\mathrm{RHL}$
$(5-\pi) b+3=(5-\pi) a+1$
$\Rightarrow 2=(a-b)(5-\pi) \Rightarrow a-b=\frac{2}{5-\pi}$