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For let h(x)={1/q if x=p/q and 0 if x...

For let `h(x)={1/q if x=p/q and 0` if x is irrational where `p & q > 0` are relatively prime integers 0 then which one does not hold good?
(a)h(x) is discontinuous for all x in `(0, oo)`
(b)h(x) is continuous for each irrational in `(0, oo)`
(c)h(x) is discontinuous for each rational in `(0, oo)`
(d)h(x) is not derivable for all x in `(0, oo)`

A

(a)h(x) is discontinuous for all x in `(0, oo)`

B

(b)h(x) is continuous for each irrational in `(0, oo)`

C

(c)h(x) is discontinuous for each rational in `(0, oo)`

D

(d)h(x) is not derivable for all x in `(0, oo)`

Text Solution

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The correct Answer is:
B
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