Question

Let f and g be differentiable function satisfying g ¢(1) = 2, g(1) = b and fog = I (Identity function) then f ¢(2) is

equal to

• A. ½
• B. 2
• C. 2/3
• D. None

Answer 1

Answer: (A)

½

Answer 2

Qfog(x) = f(g(x)) = x Ž f ¢g(x) × g ¢(x) = 1

Ž f ¢(g(x)) = $\frac{1}{g'(x)}$

for f ¢(2), g(x) = b Ž x = a (given)

\ f ¢(g(1)) =$\frac{1}{g'(a)}$Ž f ¢(2) =$\frac{1}{2}$ (Qg ¢(1) = 2(given))