If f(2x + 3) =

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

Solution:

Given f(2x + 3) = 4x2 + 12x + 15

= (2x)2 + 2(2x) (3) + (3)2 + 6

f(2x + 3) = (2x + 3)2 + 6

i.e f(y) = y2 + 6 where y = 2x + 3

∴ f (3x + 2) = (3x + 2)2 + 6

= 9x2 + 4 + 12x + 6

Hence f(3x + 2) = 9x2 + 12x + 10