Question

3

f(x) = 7x - 5x
The function is
oddlever
because
f(-x) = f(x)
f(-x) = -f(x)

Answer 1

when testing for ODD or EVEN behaviour in a function, let's recall that we check what would the original function be if we were to use the argument -x in it? well, hell let's do that and check what's cooking.

keeping in mind that if EVEN, we'll get back the original function, if ODD well get back a negative version of the original function.

`\stackrel{original}{f(x)=7x^3-5x} \\\\[-0.35em] ~\dotfill\\\\ f(~-x~)=7(-x)^3-5(-x)\implies f(~-x~)=7(-x)(-x)(-x)-5(-x) \\\\\\ f(~-x~)=7(-1)(x)(x)(x)+5x\implies f(~-x~)=-7x^3+5x \\\\\\ f(~-x~)~~ = ~~-\underset{f(x)}{(7x^3-5x)}\qquad \leftarrow \qquad \stackrel{\textit{\LARGE odd}}{\textit{negative version of the original}}`