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Omni-MATH / Determine all functions f from the reals to the reals for which (1) f(x) is strictly increasing, (2) f(x)+g(x)=2x for all real x, where g(x) is the composition inverse function to …

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problem

Determine all functions ff from the reals to the reals for which (1) f(x)f(x) is strictly increasing, (2) f(x)+g(x)=2xf(x)+g(x)=2 x for all real xx, where g(x)g(x) is the composition inverse function to f(x)f(x). (Note: ff and gg are said to be composition inverses if f(g(x))=xf(g(x))=x and g(f(x))=xg(f(x))=x for all real x.)
Plain-text mathematical notation (without MathML)
Determine all functions f from the reals to the reals for which (1) f(x) is strictly increasing, (2) f(x)+g(x)=2x for all real x, where g(x) is the composition inverse function to f(x). (Note: f and g are said to be composition inverses if f(g(x))=x and g(f(x))=x for all real x.)
Original LaTeX notation
Determine all functions $f$ from the reals to the reals for which (1) $f(x)$ is strictly increasing, (2) $f(x)+g(x)=2 x$ for all real $x$, where $g(x)$ is the composition inverse function to $f(x)$. (Note: $f$ and $g$ are said to be composition inverses if $f(g(x))=x$ and $g(f(x))=x$ for all real x.)

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Source and history

task_id
8653da4c-5e5d-5daa-b35a-348246e005e4
task_key
test--8653da4c-5e5d-5daa-b35a-348246e005e4
task_revision_id
1
config / split
/ test

Official source

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