If there b a function f(x)=g(x)+h(x), where g(x) is an odd function & h(x) is an even function, then is f(x) an odd or even function?
For example, f(x)=sgn(x)+x2
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2 Answers
1Given , g { - x } = - g { x }
And , f { x } = f { - x } , or , - f { - x } = - f { x } ,
Add them up.
f { x } + g { x } = f { - x } - g { - x }
Or , h { x } = f { - x } - g { - x }
Putting - x instead of x ,
h { - x } = f { x } - g { x } = f { - x } + g { - x }
Clearly , h { x } is neither even nor odd .
62Ratul.. a similar but often repeated question..
Prove that any function can be expressed as a sum of one even and one odd function....