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Question

Let f(x+y)=f(x)f(y) for all x and y. Suppose f(5)=2 and f(0)=3. Find f(5).

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Solution

We are given f(x+y)=f(x)f(y)...(1) for all x and y.

In the equation (1),we put x=5,y=0. Then f(5)=f(5)f(0).

This gives f(0)=1[f(5)=20].

Now f(5)=limh0f(5+h)f(5)h=limh0f(5)f(h)f(5)h by (1)

f(5)=f(5)limh0f(h)1h=f(5)limh0f(h)f(0)h[f(0)=1]

f(5)=f(5).f(0)=2×3=6

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