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2. In the terminology, a function f(x) is even when its graph is symmetric with respect to the y-axis, and odd when its graph is symmetric with respect to the origin. Prove that (a) f(x) = a,,xr+. 2n+1 .+a,x' +a,x is an odd function. (b) f(x) = a,x +a,-x-, +.+a,x +a, is an odd function. (c) The product of two even (or two odd) function is even. (d) The product of an odd function and an even function is odd.

2. In the terminology, a function f(x) is even when its graph is symmetric with respect to the y-axis, and odd when its graph is symmetric with respect to the origin. Prove that (a) f(x) = a,,xr+. 2n+1 .+a,x' +a,x is an odd function. (b) f(x) = a,x +a,-x-, +.+a,x +a, is an odd function. (c) The product of two even (or two odd) function is even. (d) The product of an odd function and an even function is odd.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
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2. In the terminology, a function f(x) is even when its graph is symmetric with respect to the y-axis, and odd when its graph is symmetric with respect to the origin. Prove that 20+1 (a) f(x) = anex +..+a,x' + a,x is an odd function. (b) f(x) = a,,x" +a,n-2x 2n-2 .+a,x' +a, is an odd function. +..... (c) The product of two even (or two odd) function is even. (d) The product of an odd function and an even function is odd.
Transcribed Image Text:2. In the terminology, a function f(x) is even when its graph is symmetric with respect to the y-axis, and odd when its graph is symmetric with respect to the origin. Prove that 20+1 (a) f(x) = anex +..+a,x' + a,x is an odd function. (b) f(x) = a,,x" +a,n-2x 2n-2 .+a,x' +a, is an odd function. +..... (c) The product of two even (or two odd) function is even. (d) The product of an odd function and an even function is odd.
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