Let f(x) be a function with domain R.(a) Show that E(x) = f(x) + f(-x) is an even function. (Simplify your answers completely.)E(-x) = f(-x) + f(-(E(x) = f(x) + f(-x) =Since E(-x) = E=Since O(-x) = -0(b) Show that O(x) = f(x) = f(-x) is an odd function. (Simplify your answers completely.)O(x) = f(x) = f(-x) U O(-x) = f-f(-(-x))f(-x) +E(x)=E is an even function.f(-x) - f(x)==-- [F(x) - ( [-O(x)=O is an odd function.

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(a) Show that E(x) = f(x) + f(-x) is an even function. (Simplify your answers completely.) E(x) = f(x) + f(-x) Since E(-x) = E lain L. E(-x) = f(-x)+ Since O(-x) = -0 = E(x) O(x) = f(x) - f(-x) => 0(-x) = (b) Show that O(x) = f(x) = f(-x) is an odd function. (Simplify your answers completely.) C ])-₁- f(-(-x)) f(-x) - f(x) == -- [₁(x)-([ -O(x) = ((1 CE f(-x)+1 = E is an even function. O is an odd function.

(a) Show that E(x) = f(x) + f(-x) is an even function. (Simplify your answers completely.) E(x) = f(x) + f(-x) Since E(-x) = E lain L. E(-x) = f(-x)+ Since O(-x) = -0 = E(x) O(x) = f(x) - f(-x) => 0(-x) = (b) Show that O(x) = f(x) = f(-x) is an odd function. (Simplify your answers completely.) C ])-₁- f(-(-x)) f(-x) - f(x) == -- [₁(x)-([ -O(x) = ((1 CE f(-x)+1 = E is an even function. O is an odd function.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

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