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Grade Upto college levelDifferential Calculus

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 agoGrade Upto college level

1 Answer

Rinkoo Gupta

12 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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