# determine whether the function f(x)=x^4+x^2+3 is even, odd, or neither.?

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This is an EVEN function

The definition of an even function is for all 'x',:

f(-x) = f(x). This means that all negative 'x' values of the function have f(x) values the same as their corresponding positive 'x' value [i.e. for the above case f(-1) = f(1) = 5]

To prove this, plug in -x for x in the function:

f(-x) = (-x)^4 + (-x)^2 + 3 -------> x^4 + x^2 + 3

Since f(-x) = f(x) = x^4 + x^2 + 3, this is an EVEN function

In general, polynomials with an even power are EVEN functions (i.e. x^2, x^4, x^6.....) whereas polynomials with odd powers are ODD functions (i.e. x, x^3, x^5.....)

ODD functions are defined as:

f(-x) = -f(x)

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Hope this helps

• An odd function does not mean that the results are always even or odd. If that's what it meant, this would be an odd function. However the definition of an odd function given by the first answer is correct and therefore this is an even function.

• f(-x)=x^4 + x^2 + 3 = f(x)

so f(x) is an even function

• Anonymous