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MATH / Let Q^(+) denote the set of positive rational numbers. Let f:Q^(+)→Q^(+) be a function such that f(x+(y)/(x))=f(x)+(f(y))/(f(x))+2yfor all x, y∈Q^(+). Find all possible values of …

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problem

Let Q+\mathbb{Q}^+ denote the set of positive rational numbers. Let f:Q+→Q+f : \mathbb{Q}^+ \to \mathbb{Q}^+ be a function such that f(x+yx)=f(x)+f(y)f(x)+2yf \left( x + \frac{y}{x} \right) = f(x) + \frac{f(y)}{f(x)} + 2yfor all x,x, y∈Q+.y \in \mathbb{Q}^+. Find all possible values of f(13).f \left( \frac{1}{3} \right). Enter all the possible values, separated by commas.
Plain-text mathematical notation (without MathML)
Let Q^(+) denote the set of positive rational numbers.  Let f:Q^(+)→Q^(+) be a function such that
f(x+(y)/(x))=f(x)+(f(y))/(f(x))+2yfor all x, y∈Q^(+).

Find all possible values of f((1)/(3)).  Enter all the possible values, separated by commas.
Original LaTeX notation
Let $\mathbb{Q}^+$ denote the set of positive rational numbers.  Let $f : \mathbb{Q}^+ \to \mathbb{Q}^+$ be a function such that
\[f \left( x + \frac{y}{x} \right) = f(x) + \frac{f(y)}{f(x)} + 2y\]for all $x,$ $y \in \mathbb{Q}^+.$

Find all possible values of $f \left( \frac{1}{3} \right).$  Enter all the possible values, separated by commas.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
3059eb82-7351-5988-9bca-513ae60a494e
task_key
intermediate~5falgebra--test--3059eb82-7351-5988-9bca-513ae60a494e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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