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Question 414471: is this function even odd or neither?
f(x)= -7 lxl + 3x^2 + 5
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First, we need to find f(-x)
f(x)= -7 |x| + 3x^2 + 5
f(-x)= -7 |-x| + 3(-x)^2 + 5
f(-x)= -7|x| + 3x^2 + 5
Note: |-x| = |-1*x| = |-1|*|x| = 1*|x| = |x| since |xy| = |x|*|y|
So f(x) = f(-x). This means that the function is even.
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Now let's find -f(x)
f(x)= -7 |x| + 3x^2 + 5
-f(x)= -(-7 |x| + 3x^2 + 5)
-f(x)= 7|x| - 3x^2 - 5
Since -f(x) does NOT equal f(-x), this means that the function is NOT odd.
So the function f(x) is only even.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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