# 3. (a) Determine whether f(x)is even or odd or neither(b) Determine whether g(x) = 5 - 4z4 +323 - 2x2 + x _ 1 is even or odd or neither(c) Show that any function can be written as the sum of an even and an odd functionShow how g(z) above can be written as the sum of an even and an odd function

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Practice Question 3.3 help_outlineImage Transcriptionclose3. (a) Determine whether f(x) is even or odd or neither (b) Determine whether g(x) = 5 - 4z4 +323 - 2x2 + x _ 1 is even or odd or neither (c) Show that any function can be written as the sum of an even and an odd function Show how g(z) above can be written as the sum of an even and an odd function fullscreen
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Step 1

Let g(x) be any function we can write it as shown below help_outlineImage Transcriptionclose1 8 (x)())(-x)(-) 1 1 (2 (x)+(-x)(2(x)-g(-x) t()()(-) ) md k()=(()-2(-3) 8 (x) f(x)+h(x) 1 (g(x)+g(-x))and h(x)=(g(x)-(-x) fullscreen
Step 2

Here f(x) and h(x) are even and o... help_outlineImage Transcriptioncloses(x)(()+g(-x)) Substitute x in f (x ) we get f(-x)=(8(-x)8(+x)) gg f(-x)=(x) Thus f(x)is an even function Mx)(s(x)-(- )) Substitute x in h (x) we get h(-x)(x)-(+x)) M(-) )-g(-)) h(-x)h(x) Thus g(x)is an odd function Thus, we can write any function g(x) as the sum of even and odd functions fullscreen

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