$g(t)$  $=$  $(t)^2  (t)^4$  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 $\,f\,$, $\,f(x) = f(x)\,$. 
$\cssId{s72}{g(x)} \cssId{s73}{= (x)^3  1} \cssId{s74}{= x^3  1}$  find $\,g(x)\,$: definition of $\,g\,$; function evaluation 
$\cssId{s77}{g(x)} \cssId{s78}{= (x^31)} \cssId{s79}{= x^3 + 1}$  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. 
PROBLEM TYPES:
