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Question

Let f(x+y)=f(x)f(y) for all x and y. If f(7)=2 and f(0)=3, then f(7) is equal to

A
5
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B
6
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C
0
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D
none of these
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Solution

The correct option is B 6
Given, f(7)=2,f(0)=3 Also, f(x+y)=f(x)f(y)

f(7)=limh0f(7+h)f(7)h
=limh0f(7)f(h)f(7)f(0)h, Since f(0)=1
=f(7)limh0f(h)f(0)h=f(7)f(0)=23=6

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