Correct Answer - Option 2 : 2x
Calculation:
g(-x) = -g(x) i.e it is an odd function.
N = pq + r (N is dividend, p is divisor, q is quotient, r is remainder)
So, g(x) = (x - 3)k + 6 ( (x - 3) is dividend, k is divisor, 6 is remainder)
when g(x) mod x2 - 9
g(x) = m(x2 - 9) + ax + b ( as if the degree of divisor is 2 (x2) ,then remainder will be of lesser degree i.e ax + b )
now at x=3
⇒ g(x) = 3a + b = 6
and x = -3 remainder will be -6
⇒ g(-3) = -3a + b=-6
⇒ 2b = 0
so, b = 0 and a = 2
remainder= ax + b = 2x
If f(x) = f(-x); It is called an even function
If f(x) = -f(-x); It is called an odd function.
Dividend = Divisor × Quotient + Remainder