`f(x)={{:(e^x+1", "-1lexgt0),(e^x", "x=0),(e^x-1", "0ltxle1):}`
Statement -1 is bounded but never attains its macimum and minimum values
Statement-2 x=0 is the point of discontinuity of f(x)

Options

A. Statement-1 is True, Statement-2 is True,Statement -2 is a correct explanation for Statement -2
B. Statement -1 True ,Statement -2 is True ,Stament -2 is not a correct explanation for Statement -!
C. Statement -1 is True Statement -2 is False
D. Statement -1 is Flase,Statement -2 is True

Answer

A

Explanation

Given that
`f(x)={{:(e^x+1", "-1lexgt0),(e^x", "x=0),(e^x-1", "0ltxle1):}`
`rArr f'(x) ={{:(e^x", "-1ltxlt0),(e^x", "0ltxlt1):}`
It is evident from the graph of f(x) that f(x) is bounded and has 2 and 0 as its maximum and minimum values . Also,f(x) does not attain these values as f(x) is not continuous at x=0
Hence , both the statements are true and statement-2 is a correct explanations of statement-1