SOLUTION: is this function even odd or neither? f(x)= -7 lxl + 3x^2 + 5

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.

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Jim

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