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OlympiadBench / 2242 / Let f(x)=2^(kx)+9, where k is a real number. If f(3):f(6)=1:3,…

Problem

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

question

Let f(x)=2kx+9f(x)=2^{k x}+9, where kk is a real number. If f(3):f(6)=1:3f(3): f(6)=1: 3, determine the value of f(9)−f(3)f(9)-f(3).
Plain-text mathematical notation (without MathML)
Let f(x)=2^(kx)+9, where k is a real number. If f(3):f(6)=1:3, determine the value of f(9)−f(3).
Original LaTeX notation
Let $f(x)=2^{k x}+9$, where $k$ is a real number. If $f(3): f(6)=1: 3$, determine the value of $f(9)-f(3)$.

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID
2242
task_id
031a202f-3778-57b0-8b8b-17f35df68209
task_key
OE~5fTO~5fmaths~5fen~5fCOMP--train--2242
task_revision_id
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import