Q.

Let f : R → R be given by f(x)=5x. If xQ and f(x)=x2+6 if xR~Q, then 

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a

f is continuous at x=3 but not at x=2

b

f is continuous at x=2 and x=3

c

f is continuous at x=2 but not at x=3

d

f is not continuous at x=2 and x=3

answer is A.

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Detailed Solution

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f (x) is continuous when 5x=x2+6
x25x+6=0x=2,3

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Let f : R → R be given by f(x)=5x. If x∈Q and f(x)=x2+6 if x∈R~Q, then