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Statement I f(x) = sin x + [x] is discon...

Statement I `f(x) = sin x + [x]` is discontinuous at x = 0.
Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

A

Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I

B

Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

C

Statement I is correct, Statement II is incorrect

D

Statement I is incorrect, Statement II is correct.

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • The function f(x)=cotx is discontinuous on the set

    A
    `{x=npi:n in Z}`
    B
    `{x=2n pi : n in Z}`
    C
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    D
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    A
    `{npi:n inZ}`
    B
    `{2npi:n in Z}`
    C
    `{(2n+1)(pi)/(2):n in Z}`
    D
    `{(npi)/(2):n in Z}`

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    Let y = f(x) be defined in [a, b], then (i) Test of continuity at x = c, a lt c lt b (ii) Test of continuity at x = a (iii) Test of continuity at x = b Case I Test of continuity at x = c, a lt c lt b If y = f(x) be defined at x = c and its value f(c) be equal to limit of f(x) as x rarr c i.e. f(c) = lim_(x to c) f(x) or lim_(x to c^(-))f(x) = f(c) = lim_(x to c^(+)) f(x) or LHL = f(c) = RHL then, y = f(x) is continuous at x = c. Case II Test of continuity at x = a If RHL = f(a) Then, f(x) is said to be continuous at the end point x = a Case III Test of continuity at x = b, if LHL = f(b) Then, f(x) is continuous at right end x = b. Max ([x],|x|) is discontinuous at

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