(b) Show that for each z E Q, we have f(x) = x. Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) andf(xy) = f(x)f(y). We proved in Tutorial 4B that then we also have f(0) = 0, f(1) = 1,f(-1) = -1, and the implication a

Answered: (b) Show that for each z EQ, we have…

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(b) Show that for each z EQ, we have f(x) =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 11E

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Question

(b) Show that for each z E Q, we have f(x) = x.

Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) and
f(xy) = f(x)f(y). We proved in Tutorial 4B that then we also have f(0) = 0, f(1) = 1,
f(-1) = -1, and the implication a<b⇒ f(a) < f(b). You may freely use these facts in
solving this question.
(a) Show that for each n = Z, we have f(n) = n.

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