JEE Main202431 Jan 2024Morning ShiftMathematicsFunctionsActual

If f x = 4 x + 3 6 x - 4 , x ≠ 2 3 and ( f o f ) ( x ) = g ( x ) , where g : R - 2 3 → R - 2 3 , then ( g o g o g ) ( 4 ) is equal to

Options

A- 19 20
B19 20
C- 4
D4

Correct answer

D. 4

Step-by-step solution

Given: f x = 4 x + 3 6 x - 4 ⇒ f o f x = 4 4 x + 3 6 x - 4 + 3 6 4 x + 3 6 x - 4 - 4 ⇒ f o f x = 16 x + 12 + 18 x - 12 24 x + 18 - 24 x + 16 ⇒ f o f x = 34 x 34 ⇒ f o f x = x ⇒ g x = x ⇒ g o g x = x ⇒ g o g o g x = x ⇒ g o g o g 4 = 4

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