determine if function

Question

. f(x) = 2x^7 – x^3 + 2 determine if function is odd or even or neither

Answer 1

f(x) is even if f(x)=f(-x)

replace x by -x and if you have the same value, then it's an even function

If f(x) = -f(-x), then it's an odd function

f(-x) = -2x⁷ + x³ + 2

except for the 2, it would be an odd function

but because of the 2, it's neither

had the 2 been 2x, it would have been an odd function

for f(x)=xⁿ where n is odd, f(x) is odd,

if n is even, then f(x) is an even function

IF the 2 had been 2x then that's the same as 2x¹ where n=1 and is odd

2 is the same as 2x⁰ where n=0

2 is an even function

the other terms with odd powers of x are odd functions

add odd functions to odd functions you get an odd function'

but add an odd to an even and it's neither an odd or even function, but you can

decompose that into its odd and even components