If f(2x + 3) =

Question:

If f(2x + 3) = 4x2 + 12x +15, then the value of f(3x + 2) is __________ .

Solution:

Given f(2+ 3) = 4x2 + 12x + 15

= (2x)2 + 2(2x) (3) + (3)2 + 6 

f(2+ 3) = (2x + 3)2 + 6

i.e  f(y) = y+ 6    where y = 2x + 3

∴  f (3x + 2) = (3x + 2)2 + 6

= 9x2 + 4 + 12x + 6

Hence f(3x + 2) = 9x2 + 12+ 10

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