Solved: Exercises 36 and 37 use the following definition: If f : R R and g: R R are

Chapter 7, Problem 37

(choose chapter or problem)

Exercises 36 and 37 use the following definition: If \(f: \mathbf{R} \rightarrow \mathbf{R}\) and \(g: \mathbf{R} \rightarrow \mathbf{R}\) are functions, then the function \((f+g): \mathbf{R} \rightarrow \mathbf{R}\) is defined by the formula ( f + g)(x) = f (x) + g(x) for all real numbers x.

If \(f: \mathbf{R} \rightarrow \mathbf{R}\) and \(g: \mathbf{R} \rightarrow \mathbf{R}\) are both onto, is f + g also onto? Justify your answer.

Text Transcription:

f: mathbf R rightarrow mathbf R

g: mathbf R rightarrow mathbf R

(f+g): mathbf R rightarrow mathbf R

f: mathbf R rightarrow mathbf R

g: mathbf R rightarrow mathbf R