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Question

Let f(x+y)=f(x)f(y) and f(x)=1+(sin2x)g(x) where g(x) is continuous, then f(x) equals

A
f(x)g(0)
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B
2f(x)g(0)
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C
2g(0)
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D
2f(0)
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Solution

The correct option is B 2f(x)g(0)

f(x)=limh0f(x+h)f(x)h


=limh0f(x)(f(h)1)h


=limh0f(x)2(sin2h(g(h)))2h


=2f(x)g(0)


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