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MATH / The function f(x)=x+1 generates the sequence

Problem

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problem

The function f(x)=x+1f(x) = x + 1 generates the sequence 1,2,3,4,…1, \ 2, \ 3, \ 4, \ \dotsin the sense that plugging any number in the sequence into f(x)f(x) gives the next number in the sequence. What rational function g(x)g(x) generates the sequence 12,23,34,45,…\frac{1}{2}, \ \frac{2}{3}, \ \frac{3}{4}, \ \frac{4}{5}, \ \dotsin this manner?
Plain-text mathematical notation (without MathML)
The function f(x)=x+1 generates the sequence
1, 2, 3, 4, …in the sense that plugging any number in the sequence into f(x) gives the next number in the sequence.

What rational function g(x) generates the sequence
(1)/(2), (2)/(3), (3)/(4), (4)/(5), …in this manner?
Original LaTeX notation
The function $f(x) = x + 1$ generates the sequence
\[1, \ 2, \ 3, \ 4, \ \dots\]in the sense that plugging any number in the sequence into $f(x)$ gives the next number in the sequence.

What rational function $g(x)$ generates the sequence
\[\frac{1}{2}, \ \frac{2}{3}, \ \frac{3}{4}, \ \frac{4}{5}, \ \dots\]in this manner?

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
25fb6cdf-3001-53a2-9b7b-62efa6f60c5e
task_key
intermediate~5falgebra--test--25fb6cdf-3001-53a2-9b7b-62efa6f60c5e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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