Odd Extension of a Function

Q.

The odd extension of the function y = $x^2$ is y = $-x^2$

1. True

2. False

Q.

$\mathrm{If}f\left(x\right)=(\begin{array}{c}{x}^3+x^2,for0\le x\le 2\\ x+2,for2\le x\le 4\end{array}$
then the odd extension of f(x) would be -

1. $f\left(x\right)=(\begin{array}{c}{x}^3+x^2,for-2\le x\le 0\\ x+2,for-4\le x\le -2\end{array}$

2. $f\left(x\right)=(\begin{array}{c}-x^3+x^2,for-2\le x\le 0\\ -x+2,for-4\le x\le -2\end{array}$

3. 
   $f\left(x\right)=(\begin{array}{c}{x}^3-x^2,for-2\le x\le 0\\ x-2,for-4\le x\le -2\end{array}$

4. $\text{None of these}$
   

Q.

Odd extension is obtained by replacing x by (-x) in the equation of f(x).

1. True

2. False