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Question

If f(x+y)=f(x).f(y) and f(5)=2, f(0)=3 then f(5) equals

A
0
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B
1
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C
6
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D
2
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Solution

The correct option is C 6
Given f(x+y)=f(x)f(y)

f(0+0)=(f(0))2

f(0)=0 or f(0)=1 but f(0)0

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

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

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

f(0)=f(0)limh0f(h)1h

3=limh0f(h)1h (f(0)=1)

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

f(5)=f(5)×3

=2×3=6

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