benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / There are real numbers a and b for which the function f has the properties that f(x)=ax+b for all real numbers x, and f(bx+a)=x for all real numbers x. What is the value of a+b?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

There are real numbers aa and bb for which the function ff has the properties that f(x)=ax+bf(x) = ax + b for all real numbers xx, and f(bx+a)=xf(bx + a) = x for all real numbers xx. What is the value of a+ba+b?
Plain-text mathematical notation (without MathML)
There are real numbers a and b for which the function f has the properties that f(x)=ax+b for all real numbers x, and f(bx+a)=x for all real numbers x. What is the value of a+b?
Original LaTeX notation
There are real numbers $a$ and $b$ for which the function $f$ has the properties that $f(x) = ax + b$ for all real numbers $x$, and $f(bx + a) = x$ for all real numbers $x$. What is the value of $a+b$?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
cec294e2-dc86-5fb0-b2ed-622f1848bcc8
task_key
test--cec294e2-dc86-5fb0-b2ed-622f1848bcc8
task_revision_id
1
config / split
/ test

Official source

initial import