Question

If f(1) = 1, f '(1) = 3 , then the derivative of f(f(f(x))) + (f(x)²) at x = 1 is:
(A) 33 (B) 15
(C) 9 (D) 12

Answer 1

Answer:

→ f(f(f(x))) + (f(x)²) = f ( f ^ 2 + 1 )

Step-by-step explanation:

f ( 1 ) = 1 , f ' ( 1 ) = 3

→ f(f(f(x))) + (f(x)²) at x = 1

f(f(f(x)) = f * ( f * ( f * 1 ) )

= f * ( f * ( f ) )

= f * ( f ^ 2 )

f(f(f(x)) = f ^ 3

(f(x)²) = f ( 1 ^ 2 )

= f ( 1 )

= f

(f(x)²) = f

→ f(f(f(x))) + (f(x)²) = f ^ 3 + f

→ f(f(f(x))) + (f(x)²) = f ( f ^ 2 + 1 )