Function again

Algebra Level 2

f ( 2 x ) = 3 + x 2 + 1 x \large f \left(\dfrac{2}{x}\right) = \dfrac{3 + x}{ 2 + \frac{1}{x}}

What is the value of 3 f ( 2 ) 3f(2) ?

Source : Mathematics Competition for Junior High School 2013, Forum Ilmiah Matematika Nasional Universitas Negeri Semarang .


The answer is 4.

Raihan Fauzan by Raihan Fauzan , 20, Indonesia

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1 solution

Raihan Fauzan
May 7, 2016

First, find the value of f ( 2 ) f(2)

f ( 2 ) = f ( 2 1 ) = 3 + 1 2 + 1 1 = 4 3 f(2) = f(\frac{2}{1}) = \frac{3 + 1}{2 + \frac{1}{1}} = \frac{4}{3}

Thus, 3 f ( 2 ) = 3 × 4 3 = 4 3f(2) = 3 \times \frac{4}{3} = \boxed{4}

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