document.write( "Question 1071547: Determine if the function is even, odd, or neither.
\n" ); document.write( "f(x) = -4x3 + 7x
\n" ); document.write( "please explain in detail how to solve this I really want to understand it thank you. \n" ); document.write( "

Algebra.Com's Answer #686468 by math_helper(2461) $\"\"$ $\"About$

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Even functions have the property f(-x) = f(x) over all x in the domain of f.
\n" ); document.write( "Odd functions have the property f(-x) = -f(x) over all x in the domain of f.
\n" ); document.write( "--
\n" ); document.write( " $\"+f%28x%29=x%5E2+\"$ is an example of an even function because f(-x) = f(x)
\n" ); document.write( " Try it: $\"+f%28-4%29+=+%28-4%29%5E2+=+16+=+%284%29%5E2+=+f%284%29+\"$
\n" ); document.write( "--
\n" ); document.write( " $\"++f%28x%29=x%5E3+\"$ is an example of an odd function because f(-x) = -f(x)
\n" ); document.write( " Try it: $\"+f%28-2%29+=+%28-2%29%5E3+=+-8+=+-%282%5E3%29=+-f%282%29+\"$
\n" ); document.write( "—
\n" ); document.write( "On to the problem at hand: $\"+f%28x%29=-4x%5E3+%2B+7x+\"$ \r
\n" ); document.write( "\n" ); document.write( "Let's look at f(-x) and see how that relates to f(x):
\n" ); document.write( " $\"+f%28-x%29+=+-4%28-x%5E3%29+%2B+7%28-x%29+\"$
\n" ); document.write( "= $\"+-4%28-1%5E3%29%28x%5E3%29+-+7x+\"$
\n" ); document.write( "= $\"++4x%5E3+-+7x+\"$
\n" ); document.write( "= $\"+-%28-4x%5E3+%2B+7x%29+\"$
\n" ); document.write( "The part in the parenthesis is nothing more than f(x):
\n" ); document.write( "= $\"++-f%28x%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Since f(-x) = -f(x) this function is an odd function.
\n" ); document.write( "—
\n" ); document.write( "Ans: $\"+f%28x%29+=+-4x%5E3+%2B+7x+\"$ is an ODD function.
\n" ); document.write( "—\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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