Question

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.

Accepted Answer

@#LAT-DLM& is one-to-one. Proof: Let @#LAT-DLM& and @#LAT-DLM& be any

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.

Speaking Mathematically

The Logic of Compound Statements

The Logic of Quantified Statements

Elementary Number Theory and Methods of Proof

Sequences, Mathematical Induction, and Recursion

Set Theory

Relations

Counting and Probability

Graphs and Trees

Analyzing Algorithm Efficiency

Regular Expressions and Finite State Automata

Filters

Exam 7: Functions

Define a function f:R−{0}⟶Rf : \mathbf { R } - \{ 0 \} \longrightarrow \mathbf { R }f:R−{0}⟶R by the formula f(x)=x+3xf ( x ) = \frac { x + 3 } { x }f(x)=xx+3​ for all nonzero real numbers xxx . Prove that fff is one-to-one.