If f(x) = 2^x, what is the value of f(x+1) + f(x)f(x)?

f(x + 1) + f(x)f(x) = f(x + 1)f(x) + 1 = 2^x+12^x + 1 = 2^1 + 1 = 3.

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South African Mathematics Olympiad Second Round

South Africa algebra

Problem

f (x) = 2^{x}

, what is the value of

\frac{f ( x + 1 ) + f ( x )}{f ( x )}

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.

Final answer

Techniques

Exponential functions