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Byju's Answer
Standard XII
Mathematics
Derivative
If f2 x+3=4 x...
Question
If f(2x + 3) = 4x
2
+ 12x +15, then the value of f(3x + 2) is __________ .
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Solution
Given f(2x + 3) = 4x
2
+ 12x + 15
=
(2x)
2
+ 2(2x) (3) + (3)
2
+ 6
f(2x + 3) = (2x + 3)
2
+ 6
i.e f(y) = y
2
+ 6 where y = 2x + 3
∴ f (3x + 2) = (3x + 2)
2
+ 6
= 9x
2
+ 4 + 12x + 6
Hence f(3x + 2) = 9x
2
+ 12x + 10
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