If $F(x+y) = F(x) * F(y)$
Given: $F(3) = 729$
Find $F(1/2) + F(1) + F(3/2) = ?$

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Explanation

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Official Explanation

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We are given

F(x+y) = F(x) \cdot F(y)

and

F(3) = 729

.

First, find

F(3/2)

F(3) = F\left(\frac{3}{2} + \frac{3}{2}\right) = F\left(\frac{3}{2}\right) \cdot F\left(\frac{3}{2}\right) = \left[F\left(\frac{3}{2}\right)\right]^2 = 729

\Rightarrow F\left(\frac{3}{2}\right) = \sqrt{729} = 27

Next, find

F(1)

F(3) = F(1 + 1 + 1) = F(1) \cdot F(1) \cdot F(1) = [F(1)]^3 = 729

…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.