Mathematics

Question

is
-f(x)
the same as
f(-x)

1 Answer

  • Answer:

      In general, no.

    Step-by-step explanation:

    f(-x) = -f(x) when the function is "odd." Such a function is symmetrical about the origin. This will not generally be the case, so, in general, -f(x) ≠ f(-x).

    _____

    Additional comment

    When f(-x) = f(x), the function is "even." It is symmetrical about the y-axis.

    Among trig functions, sin(x) is odd, and cos(x) is even.

    Among polynomials, any polynomial with only odd-degree terms is odd; any polynomial with only even-degree terms is even.

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