Answer
a. Neither
b. Odd
c. Even
d. Neither
Work Step by Step
a. $f(x) = 2x^5 - 3x^2 + 2$
$f(-x) = 2(-x)^5 - 3(-x)^2 + 2$
$f(-x) = -2x^5 - 3x^2 + 2$
Neither
b. $f(x) = x^3 - x^7$
$f(-x) = (-x)^3 - (-x)^7$
$f(-x) = -x^3 + x^7 = -f(x)$
Odd
c. $f(x) = \frac{1-x^2}{1+x^2}$
$f(-x) = \frac{1-(-x)^2}{1+(-x)^2}$
$f(-x) = \frac{1-x^2}{1+x^2} = f(x)$
Even
d. $f(x) = \frac{1}{x+2}$
$f(-x) = \frac{1}{-x + 2}$
Neither