Math, asked by ashishg2, 1 year ago

the function f(x) - f(-x) is an even or odd or both

Answers

Answered by QGP

Let g(x) = f(x) - f(-x)

Now, let's check if g(x) is an odd function or even function.

Replace x→(-x)
g(-x) = f(-x) - f(-(-x))
So, g(-x) = f(-x) - f(x)
So, g(-x) = -[ f(x) - f(-x) ]
So, g(-x) = - g(x)

Clearly, g(x) is an odd function.

Thus, f(x) - f(-x) is always an odd function.

ashishg2: then density1s answer is wrong??

ashishg2: confused, who is right?

QGP: Density1 is wrong. He probably doesn't know the concept of even and odd functions

QGP: I can assure you of my answer being correct

QGP: I'm in class 12, and have a good grasp over functions.

ashishg2: a lot of thank, yar

QGP: Welcome

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