Question

If g(x) is a polynomial satisfying g(x) g(y) = g(x) + g(y) + g(xy) - 2 for all real x and y and g(2) = 5, then g(3) is equal to

• A. 10
• B. 24
• C. 21
• D. 15

Answer 1

The correct option is A 10

$g\left(x\right)g\left(y\right)=g\left(x\right)+g\left(y\right)+g\left(xy\right)-2$

$g\left(2\right)=5$

$Substituting,$

$x=2,y=1$

$g\left(1\right)g\left(2\right)=g\left(1\right)+g\left(2\right)+g\left(2\right)-2$

$g\left(1\right)5=g\left(1\right)+5+5-2$

$g\left(1\right)\left(5\right)=g\left(1\right)+8$

$g\left(1\right)\left(5\right)-g\left(1\right)=8$

$g\left(1\right)(5-1)=8$

$g\left(1\right)=2$

$g\left(1\right)=1^2+1$

$g\left(2\right)=5=2^2+1$

$Similarly,$

$g\left(3\right)=3^2+1$$=10$

$g\left(3\right)=10$