2.28. Linear function * Show that if a function satisfies f(a) + f(b) = f(a+b), then f(x) = rf (x) for any x and for any rational number r.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 58E
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Question 2.28 in the image.

2.28. Linear function *
Show that if a function satisfies f(a) + f(b) = f(a+b), then f(x) =
rf (x) for any x and for any rational number r.
Transcribed Image Text:2.28. Linear function * Show that if a function satisfies f(a) + f(b) = f(a+b), then f(x) = rf (x) for any x and for any rational number r.
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