Define a Function $f : \mathbf { R } - \{ 0 \} \longrightarrow \mathbf { R }$

question 21

Essay

Define a function $f : \mathbf { R } - \{ 0 \} \longrightarrow \mathbf { R }$ by the formula $f ( x ) = \frac { x + 3 } { x }$ for all nonzero real numbers $x$ . Prove that $f$ is one-to-one.

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Definitions:

Framing

In social psychology, the way information is presented to the audience, which influences the choices people make by highlighting certain aspects and downplaying others.

Belief Perseverance

The tendency to maintain a belief even after the evidence supporting it has been discredited or refuted.

Overconfidence

The phenomenon where an individual's belief in their own abilities exceeds the accuracy of those abilities.

Framing Effect

A cognitive bias where people react differently based on the way information is presented to them, demonstrating how context and framing can influence decision making.