Question
If f(x – 1) = 3x2 + 5x + 6, find the value of f(x + 1).
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
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:
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
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