A function $\,f\,$ is even  if and only if 
for all $\,x\,$ in the domain of $\,f\,$, $\,f(x) = f(x)\,$. 
$g(t)$  $=$  $(t)^2  (t)^4$  definition of $\,g\,$; function evaluation 
$=$  $t^2  t^4$  simplify  
$=$  $g(t)$  definition of $\,g$ 
A function $\,f\,$ is odd  if and only if 
for all $\,x\,$ in the domain of $\,f\,$, $\,f(x) = f(x)\,$. 
$g(x) = (x)^3  1 = x^3  1$  find $\,g(x)\,$: definition of $\,g\,$; function evaluation 
$g(x) = (x^31) = x^3 + 1$  find the opposite of $\,g(x)\,$: definition of $\,g\,$; the distributive law 
$f(x) = f(x)$  requirement for an odd function 
$f(0) = f(0)$  let $\,x = 0$ 
$f(0) = f(0)$  the opposite of zero is zero 
$2f(0) = 0$  add $\,f(0)\,$ to both sides 
$f(0) = 0$  divide both sides by $\,2$ 
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
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