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Prove that the square of an even or odd function is always even

Prove that the square of an even or odd function is always even

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
8 years ago
Hello Student,

f(-x)=f(x)
let g(x)= (f(x))^2
=>Replacing x by -x we get
g(-x)=(f(-x))^2
=> g(-x)=( f(x) )^2
=> g(-x)=g(x)
let f(x) is an odd function
then by def f(-x)= -f(x)
let g(x)=(f(x))^2
Replacing x by -x we get
g(-x)=(f(-x))^2
=>g(-x)=(-f(x))^2=(f(x))^2
=>g(-x)= (g(x))^2
prooved.

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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