If the function f(x)=casesa|-x|+1, & x5|x-|+3, & x5cases is continuous at x=5, then the v…

Question

If the function $f(x)=\begin{cases}a|\pi-x|+1, & x\le5\b|x-\pi|+3, & x>5\end{cases}$ is continuous at $x=5$, then the value of $a-b$ is:

Accepted Answer

RHL $=b(5-\pi)+3$; $f(5)=$ LHL $=a(5-\pi)+1$.

Continuity: $a(5-\pi)+1=b(5-\pi)+3\Rightarrow(a-b)(5-\pi)=2\Rightarrow a-b=\dfrac{2}{5-\pi}$.

Solutions · 1