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