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Define f(x) as the product of two real f...

Define `f(x)` as the product of two real functions `f_(1)(x)=x, x epsilon R` and `f_(2)(x)={("sin"1/x, "if", x!=0),(0 , "if", x=0):}` as follows `f(x)={(f_(1)(x).f_(2)(x), "if", x!=0),(0, "if", x=0):}` Statement 2: `f_(1)(x)` and `f_(2)(x)` are continuous on IR.

A

Statement-1 is True, Statement -2 is True, Statement -2 is True and Statement -2 is a correct explanation for statement -1.

B

Statement -1 is True, Statement -2 is True and Statement -2 is Not is a correct explanation for Statement -1.

C

Statement -1 is True, Statement -2 is False.

D

Statement -1 is False, Statement -2 is True.

Text Solution

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The correct Answer is:
D
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