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Question

f(x)=2x+216if x24x16kif x=2at x=2

If f(x) is continuous at x=2, then find the value of k.

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Solution

We have, f(x)={2x+2164x16if x2kif x=2

Since, f(x) is continuous at x=2.
LHL = RHL =f(2)

At x=2,
limx22x.22244x42=limx24.(2x4)(2x)(4)2=limx24.(2x4)(2x4)(2x+4) [a2b2=(a+b)(ab)]=limx24(2x+4=48=12

But f(2)=k
k=12


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