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.

---

Definitions:

Consumer Surplus

The variance between the aggregate amount consumers intend and have the means to pay for a good or service and the sum they actually pay.

Consumer Surplus

The gap between what consumers are prepared and able to spend on a product or service and the actual amount they end up paying.

Perfect Price Discriminator

A theoretical entity that charges each consumer the maximum price they would be willing to pay for a good or service.

Perfectly Competitive Firm

A company that operates in a market where buyers and sellers are so numerous and well informed that all elements of monopoly are absent, and the market price of goods is beyond the control of individual buyers and sellers.