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OlympiadBench / 2289 / Suppose that f(a)=2a²−3a+1 for all real numbers a and …

Problem

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

question

Suppose that

f(a)=2 a^{2}-3 a+1

for all real numbers

a

and

g(b)=\log _{\frac{1}{2}} b

for all

b>0

. Determine all

\theta

with

0 \leq \theta \leq 2 \pi

for which

f(g(\sin \theta))=0

Plain-text mathematical notation (without MathML)

Suppose that f(a)=2a²−3a+1 for all real numbers a and g(b)=log_((1)/(2))b for all b>0. Determine all θ with 0≤θ≤2π for which f(g(sinθ))=0.

Original LaTeX notation

Suppose that $f(a)=2 a^{2}-3 a+1$ for all real numbers $a$ and $g(b)=\log _{\frac{1}{2}} b$ for all $b>0$. Determine all $\theta$ with $0 \leq \theta \leq 2 \pi$ for which $f(g(\sin \theta))=0$.

answer type

Numerical

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2289
task_id: 99d2cd56-080c-5be3-bf29-1b9dd72390e8
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2289
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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