Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.1 AIME Find the answer South Africa

If $f(x) = 2^x$ , what is the value of $\frac{f(x+1) + f(x)}{f(x)}$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$\frac{f(x + 1) + f(x)}{f(x)} = \frac{f(x + 1)}{f(x)} + 1 = \frac{2^{x+1}}{2^x} + 1 = 2^1 + 1 = 3.$

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