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Question

Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y R and f(x)=1+xg(x), where limx0g(x)=1, then f(x) is equal to

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

The correct option is B f(x)

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

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

=f(x)limh0f(h)1h

=f(x)limh0g(h), (f(x)=1+xg(x))

=f(x) (limx0g(x)=1)

f(x)=f(x)


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