document.write( "Question 36056: 1. A function f is called even if f(-x)= f(x) and it is called odd if f(-x)= -f(x). Show that every function f can be written as the sum of an even function and an odd function. \n" ); document.write( "

Algebra.Com's Answer #22081 by kev82(151) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hi,\r
\n" ); document.write( "\n" ); document.write( "Let $\"f%28x%29\"$ be any reasonably nice function.\r
\n" ); document.write( "\n" ); document.write( "Consider $\"g%28x%29=%28f%28x%29%2Bf%28-x%29%29%2F2\"$ is it even, odd, or neither?\r
\n" ); document.write( "\n" ); document.write( "Similarly consider $\"h%28x%29=%28f%28x%29-f%28-x%29%29%2F2\"$ is it even, odd, or neither?\r
\n" ); document.write( "\n" ); document.write( "Check that $\"f=g%2Bh\"$ and there lies your answer.\r
\n" ); document.write( "\n" ); document.write( "Hope that helps,\r
\n" ); document.write( "\n" ); document.write( "Kev \n" ); document.write( "

\n" );