determine whether the function f(x)=x^4+x^2+3 is even, odd, or neither.?
- JSAMLv 51 decade agoFavorite Answer
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)
Hope this helps
- 1 decade ago
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.
- James ChanLv 41 decade ago
f(-x)=x^4 + x^2 + 3 = f(x)
so f(x) is an even function
- Anonymous1 decade ago
Odd. The last +3 gives it away.
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- cosmeLv 44 years ago
a million: Even #2: consumer-friendly HOW: Even: f(x) = f(-x) consumer-friendly: f(-x) = -f(x) attempt #a million: f(x) = 2x² - 3 f(-x) = 2(-x)² - 3 = 2x² - 3............... (when you consider that unfavorable decision squared are an same as their opposite squared) hence, it truly is even. attempt #2 f(x) = -2x^3 + 8x = x( 8 - 2x²) f(-x) = -x( 8 - 2(-x)² ) = -x( 8 - 2x²) = -f(x) hence, it truly is consumer-friendly.