Odd Extension of a Function

Q. The equation of common †an gents to the circles x2+y2-2x-6y+9=0 and x2+y2+6x-2y+1=0 is/ar 1. x=0 2. y -4=0 3. 3x+4y=10 4. 4x-3y=0

Q. If $g:[2:2]\to R$ where $g\left(x\right)=x^3+tanx+\left[\frac{x^2+1}{p}\right]$ is a odd function then the value of parametric P is where [.] denotes the Greatest integer function.

1. -5<P<5
2. None of these
3. P<5
4. P>5

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.

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

1. True

2. False

Q.

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

1. True

2. False

Q. If the roots of the quadratic equation x^2 + px + q = 0 are tan 30 and tan 15 respectively, then the value of 2+q-p is

Q. f(x) = 2x^2 - 1 is one - one for the domain _____.

1. I
2. R
3. R - N
4. N