Function and Polynomial

Which is correct statement ?

• $if\ a\ polynomial\ f\left(x\right),\ f\left(a\right)=0\ then\ \left(x-a\right)\ is\ a\ factor\ of\ f\left(x\right)$

• $f=\left\{\left(2,4\right),\left(3,5\right),\left(5,7\right)\right\}\ then\ f^{-1}=\left\{\left(\text{4,2}\right),\left(5,3\right),\left(7,5\right)\right\}$

• $both\ are\ correct$

• $both\ are\ wrong$

 $if\ g=\left\{\left(1,2\right),\left(2,3\right),\left(3,4\right)\right\}and\ h=\left\{\left(2,3\right),\left(3,4\right),\left(4,5\right)\right\}\ then\ hog=?$  

•  $\left\{\left(1,3\right),\left(2,4\right),\left(3,5\right)\right\}$  

•  $\left\{\left(3,1\right),\left(4,2\right),\left(5,3\right)\right\}$  

•  $\left\{\left(1,2\right),\left(2,3\right),\left(3,4\right)\right\}$  

•  $\left\{\left(2,1\right),\left(3,2\right),\left(4,3\right)\right\}$  

 $if\ g\left(x\right)=2x-1\ and\ f\left(x\right)=4x\ find\ the\ value\ of\ gof\left(2\right)=?$  

•  $8x-1$  

• 15

• 14

• 17

 $find\ f^{-1}\left(x\right),if\ f\left(x\right)=4x+5$  

•  $\frac{x+5}{4}$  

•  $\frac{y-5}{4}$  

•  $\frac{5x}{4}$  

•  $\frac{x-5}{4}$  

 $if\ f\left(x\right)=3x-2\ and\ fog\left(x\right)=6x-2\ then\ g\left(x\right)=?$  

•  $6x$  

•  $2x$  

•  $\frac{4x}{3}$  

•  $18x-14$  

 $if\ f\left(x\right)=2x+1\ and\ g\left(x\right)=\frac{x-5}{2}then\ f^{-1}g^{-1}\left(3\right)=?$  

•  $5$  

•  $6$  

•  $1$  

•  $x+2$  

 $if\ x-5\ is\ a\ factor\ of\ x^3+px^2+4x+5,find\ the\ value\ of\ p.$  

•  $6$  

•  $0$  

•  $-6$  

•  $5$  

 $if\ f\left(x\right)=3x-11,find\ f^{-1}\left(4\right)=?$  

•  $5$  

•  $\frac{7}{3}$  

•  $\frac{x+11}{3}$  

•  $\frac{44}{3}$  

 $if\ f\left(x\right)=2x-5,g\left(x\right)=\frac{3x+5}{2}\ and\ ff\left(x\right)=g^{-1}\left(x\right)\ then\ find\ the\ value\ of\ x.$  

•  $\frac{2x-5}{3}$  

•  $-15$  

•  $10$  

• 4

If g: A → B and f: B→ C be the two functions then what will denote the composite function from A to C?

• go(x)

• fog(x)

• gof(x)

• gog(x)