Is the function f(x) = 2x - |x| odd or even?

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A function f(x) is even if f(-x) = f(x) and odd if f(-x) = -f(x)

Here we have f(x) = 2x - |x|

For x >= 0, we have |x| = x, this gives f(x) = 2x - x = x

But for x < 0, we have |x|= (-x),...

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A function f(x) is even if f(-x) = f(x) and odd if f(-x) = -f(x)

Here we have f(x) = 2x - |x|

For x >= 0, we have |x| = x, this gives f(x) = 2x - x = x

But for x < 0, we have |x|= (-x), this gives f(x) = 2x - (-x) = 3x

So f(x) = x if x > 0 and f(x) = 3x if x < 0

This means f(-x) is neither equal to f(-x) nor equal to -f(x).

The function f(x) = 2x - |x| is neither odd nor is it even.

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