If $$f(x)f(y)=f(x+y)$$ for all x,y, suppose $$f(5)=2$$ and $$f1(0)=3$$, then $$f(5)$$ is equal to

Question

If $$f(x)f(y)=f(x+y)$$ for all x,y, suppose $$f(5)=2$$ and $$f1(0)=3$$,  then $$f(5)$$ is equal to

Infinity Learn · Accepted Answer

$$f(x+y)=f(x)f(y)$$⇒             $$f(0+5)$$  $$=$$ $$f(0)f(5)$$     ⇒   $$f(0)=1$$          ∴$$f(5)=2$$≠$$0Also$$,       $$f(5)=limh$$→$$0f(5+h)$$−$$f(5+0)h$$                                      $$=limh$$→$$0f(5)f(h)$$−$$f(5)f(0)h$$                              $$=$$ $$f(5)limh$$→$$0f(h)$$−$$f(0)h$$                             $$=$$ $$f(5)f1(0)=2$$×$$3=6Hence$$ $$(1)is$$ the correct answer.

$If f (x) f (y) = f (x + y) for all x, y, suppose f (5) = 2 and f^{1} (0) = 3,$ $t h e n f (5) i s e q u a l t o$

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If f(x)f(y)=f(x+y) for all x,y, suppose f(5)=2 and f1(0)=3, then f(5) is equal to

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$If f (x) f (y) = f (x + y) for all x, y, suppose f (5) = 2 and f^{1} (0) = 3,$ $t h e n f (5) i s e q u a l t o$