Solved: Exercises 38 and 39 use the following definition: If f : R R is a function and c

Chapter 7, Problem 38

(choose chapter or problem)

Exercises 38 and 39 use the following definition: If \(f: \mathbf{R} \rightarrow \mathbf{R}\) is a function and c is a nonzero real number, the function \((c \cdot f): \mathbf{R} \rightarrow \mathbf{R}\) is defined by the formula \((c \cdot f)(x)=c \cdot f(x)\) for all real numbers x.

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a function and c a nonzero real number. If f is one-to-one, is \(c \cdot f\) also one-to-one? Justify your answer.

Text Transcription:

f: mathbf R rightarrow mathbf R

(c cdot f): mathbf R rightarrow mathbf R

(c cdot f)(x)=c cdot f(x)

f: mathbf R rightarrow mathbf R

c cdot f