document.write( "Question 54736: If f(–x) = –f(x) for all choices of x, then what does that tell you about the function f?
\n" ); document.write( "Give an example of a function that has this property f(–x) = –f(x) for all real numbers x. \n" ); document.write( "

Algebra.Com's Answer #36968 by psbhowmick(878) $\"\"$ $\"About$

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If f(-x) = -f(x), then f(x) is called an odd function. Moreover the graph of y = f(x) is anti-symmetric about y-axis.\r
\n" ); document.write( "\n" ); document.write( "Example: f(x) = sin(x), f(x) = tan(x), $\"f%28x%29+=+x%2F%28x%5E2%2B1%29\"$ etc.\r
\n" ); document.write( "\n" ); document.write( "Proof: f(x) = sin(x), so f(-x) = sin(-x) = -sin(x) = -f(x) [for any value of 'x'] \n" ); document.write( "

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