the function f(x) - f(-x) is an even or odd or both
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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.
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??
confused, who is right?
Density1 is wrong. He probably doesn't know the concept of even and odd functions
I can assure you of my answer being correct
I'm in class 12, and have a good grasp over functions.
a lot of thank, yar
Welcome
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