Question 74

Consider the function $$f: (0, \infty) \rightarrow R$$ defined by $$f(x) = e^{-|\log_e x|}$$. If $$m$$ and $$n$$ be respectively the number of points at which $$f$$ is not continuous and $$f$$ is not differentiable, then $$m + n$$ is

f(x)=e^{-|ln x|}. For x>0: |ln x|=ln x if x≥1, -ln x if 0

f(x)=e^{-ln x}=1/x for x≥1. f(x)=e^{ln x}=x for 0

f is continuous everywhere (including x=1). m=0.

At x=1: left derivative=1, right derivative=-1. Not differentiable. n=1.

m+n=0+1=1.

The answer is Option (3): 1.

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