simple-problem-just-want-a-better-way-of-proving-this-problem-to-convince-and-satisfy-myself-in-a-better-way

Question

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

Rinkoo Gupta · Accepted Answer

let f(x) is an even functionthen by def f(-x)=f(x)let g(x)= (f(x))^2=>Replacing x by -x we getg(-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 functionthen by def f(-x)= -f(x)let g(x)=(f(x))^2Replacing x by -x we getg(-x)=(f(-x))^2=>g(-x)=(-f(x))^2=(f(x))^2=>g(-x)= (g(x))^2In this way we see that the squqre of an even or odd function is always an even function.Thanks & RegardsRinkoo GuptaAskIITians faculty

Differential Calculus> simple-problem-just-want-a-better-way-of-...

Preetam Bhowmick , 11 Years ago

Rinkoo Gupta

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Differential Calculus> simple-problem-just-want-a-better-way-of-...

Preetam Bhowmick , 11 Years ago

Rinkoo Gupta

Provide a better Answer & Earn Cool Goodies

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