If f(x – 1) = 3x2 + 5x + 6, find the value of f(x + 1).
Options:
A . 3x2 + 17x + 28
B . 3x2 + 17x – 28
C . 3x2 + 16x + 25
D . 3x2 - 16x + 25
E . 3x2 + 17x – 32
Answer: Option A : A option (a)f(x-1) = 3x2 + 5x + 6put x = x + 2, f(x + 2 – 1) = 3(x+2)2 + 5(x+2) + 6f( x + 1)= 3(x2 + 4 + 4x) + 5x + 16= 3x2 + 12 + 12x + 5x + 16= 3x2 + 17x + 28Hence option (a)Shortcut:-Assumption method Assume x = 1f(0) = 14, f(2) = 48Among the answer options, Sub x=1 and check where you are getting 48,This is obtained only at option (a)Shortcut of a shortcut!Put x=1 in the question and x=-1 in the option, both should give 14
