document.write( "Question 1113891: Determine analytically if the following functions are even, odd, or neither.
\n" ); document.write( "a. f(x) = 5x ^3 – 2x
\n" ); document.write( " b. f(x) = x ^2 + 3x – 2 \n" ); document.write( "

Algebra.Com's Answer #728969 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "Replace $\"x\"$ with $\"-x\"$ and compare the result to $\"f%28x%29\"$ .
\n" ); document.write( "If $\"f%28-x%29+=+f%28x%29\"$ , the function is $\"even\"$ .
\n" ); document.write( "If $\"f%28-x%29+=+-+f%28x%29+\"$ , the function is $\"odd\"$ .
\n" ); document.write( "If $\"f%28-x%29+%3C%3E+f%28x%29+\"$ and $\"f%28-x%29+%3C%3E+-f%28x%29+\"$ , the function is $\"neither+\"$ $\"even+\"$ $\"nor\"$ $\"+odd\"$ .\r
\n" ); document.write( "\n" ); document.write( "Remember that $\"%28-x%29%5En=x%5En\"$ if $\"n\"$ is even, and $\"%28-x%29%5En=-x%5En\"$ if $\"n\"$ is odd\r
\n" ); document.write( "\n" ); document.write( "So, in your case we have:
\n" ); document.write( "a. $\"f%28x%29+=+5x+%5E3+-+2x\"$ … replace $\"x\"$ with $\"-x\"$
\n" ); document.write( " $\"f%28-x%29+=+5%28-x%29+%5E3+-2%28-x%29\"$
\n" ); document.write( " $\"f%28-x%29+=+-5x%5E3+%2B2x\"$ …..since $\"f%28-x%29+=+-+f%28x%29+\"$ , the function is $\"odd\"$ \r
\n" ); document.write( "\n" ); document.write( "b. \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+x+%5E2+%2B+3x+-+2\"$
\n" ); document.write( " $\"f%28-x%29+=+%28-x+%29%5E2+%2B+3%28-x%29+-+2\"$
\n" ); document.write( " $\"f%28x%29+=+x+%5E2+-3x+-+2\"$ ….since $\"f%28-x%29+%3C%3E+f%28x%29+\"$ and $\"f%28-x%29+%3C%3E+-f%28x%29+\"$ , the function is $\"neither+\"$ $\"even+\"$ $\"nor\"$ $\"+odd\"$ .\r
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