sol_even_odd_1 - (f g is also even e~" C><~...

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Free From www.analyzemath.com Calculus Worksheet: Even and Odd Functions (1) 1. 1 is an even function and g is an odd function. Show that a) (I· g)( x) is an odd function. -t ~ve", -) -H -><) ~ fc><) ; d a-dd -) ~ (- ,,) -:0 - ~(,,) \ eJ-- \0 Gc" ~ Cf . ~ ) (AI):: {' (x) ~ ()() h(-><I ~ H-~\o ~(-,,) ::: {Lx). Hf)Q<') ::- ti?<l~lY) '" (_ )() = _ ~ tt ) h (>c) -= ~ . ~) &) \ s o-d c{ . b) (1/ g)(x) is an odd function. 2. Show that 1 (I x I) is an even function. \~\- 'n0'I~ -fG K\) . 'n t->'-):: J (\-"\~" '" ~ \ -::: "" G:- y') ==) r-Cx) - -+ 0 )< I ) y,0"C-e 1- >< \ = \" I In 0<' = -f (I x \) IS eJe'vL
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Free From www.analyzemath.com 3. Show that iff and g are even functions, then
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Unformatted text preview: (f + g) is also even. \ e~ '" C><~ ~ (1 + ")) (;><) ~ t (><)-+ ~ 6< ) h (-l<) ~ + (_,,) + ~ (-X) '" +(x!-t ~ 6< l1f. . .J J eve,,:-=) \t, (x) L "'" ~ x) =) h. 6'-) = ~-k-~) & I \~J-ev€\/\ . 4. Show that iff and g are odd functions, then (f + g) is also odd. k-G< \:: (J-+ ") ) (><):: fz,-) + ~J (x) II ~ J ~1~1d 8-le-G )<) '" 1 t- x)-+ () (-x)-:=-t H- ()( X) k-(-x)-:: -(f(><.) T ~G))=-\2-6<) =') \2-(x) = C --\'-'c")) &) I> o~J Free From www.analyzemath.com...
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