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Omni-MATH / A function f(x₁,x₂,…,x_(n)) is linear in each of the x_(i) and f(x₁,x₂,…,x_(n))=(1)/(x₁x₂⋯x_(n)) when x_(i)∈{3,4} for all i. In terms of n, what is f(5,5,…,5)?

Problem

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problem

A function f(x1,x2,…,xn)f\left(x_{1}, x_{2}, \ldots, x_{n}\right) is linear in each of the xix_{i} and f(x1,x2,…,xn)=1x1x2⋯xnf\left(x_{1}, x_{2}, \ldots, x_{n}\right)=\frac{1}{x_{1} x_{2} \cdots x_{n}} when xi∈{3,4}x_{i} \in\{3,4\} for all ii. In terms of nn, what is f(5,5,…,5)f(5,5, \ldots, 5)?
Plain-text mathematical notation (without MathML)
A function f(x₁,x₂,…,x_(n)) is linear in each of the x_(i) and f(x₁,x₂,…,x_(n))=(1)/(x₁x₂⋯x_(n)) when x_(i)∈{3,4} for all i. In terms of n, what is f(5,5,…,5)?
Original LaTeX notation
A function $f\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ is linear in each of the $x_{i}$ and $f\left(x_{1}, x_{2}, \ldots, x_{n}\right)=\frac{1}{x_{1} x_{2} \cdots x_{n}}$ when $x_{i} \in\{3,4\}$ for all $i$. In terms of $n$, what is $f(5,5, \ldots, 5)$?

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Source and history

task_id
d2518b91-c625-5603-be50-6aaaaecc25eb
task_key
test--d2518b91-c625-5603-be50-6aaaaecc25eb
task_revision_id
1
config / split
/ test

Official source

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