Question 414471
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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