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OlympiadBench / 2248 / The functions f and g satisfy

Problem

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

answer type

Numerical

is multiple answer

false

language

English

question

The functions

f

and

g

satisfy

$$
\begin{aligned}
& f(x)+g(x)=3 x+5 \\
& f(x)-g(x)=5 x+7
\end{aligned}
$$

for all values of

x

. Determine the value of

2 f(2) g(2)

Plain-text mathematical notation (without MathML)

The functions f and g satisfy

$$
\begin{aligned}
& f(x)+g(x)=3 x+5 \\
& f(x)-g(x)=5 x+7
\end{aligned}
$$

for all values of x. Determine the value of 2f(2)g(2).

Original LaTeX notation

The functions $f$ and $g$ satisfy

$$
\begin{aligned}
& f(x)+g(x)=3 x+5 \\
& f(x)-g(x)=5 x+7
\end{aligned}
$$

for all values of $x$. Determine the value of $2 f(2) g(2)$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2248
task_id: 6e91a442-510b-5924-ace3-16bb4328bf77
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2248
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import