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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

Preetam Bhowmick , 12 Years ago
Grade Upto college level
anser 1 Answers
Rinkoo Gupta

Last Activity: 11 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
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