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Prove that the square of an even or odd function is always even . I have solved this myself but i am not that convinced with my way so i just want you to do it so that i can compare your solution with mine to improve myself at those points in the solution. thank you will be awaiting for your reply eagerly

Prove that the square of an even or odd function is always even . I have solved this myself but i am not that convinced with my way so i just want you to do it so that i can compare your solution with mine to improve myself at those points in the solution. thank you will be awaiting for your reply eagerly

Grade:Upto college level

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
let f(x) is an even 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 since f(x) is an even fn.
=> g(-x)=g(x)
Now,
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
In this way we see that the squqre of an even or odd function is always an even function.

Thanks & Regards
Rinkoo Gupta
AskIITians faculty

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