Question

If the function  then the value ofg’(1) is

Solution

Correct option is

2

Since g(x) = f –1 (x) so f (g(x)) = x for all x. differentiating

f’(g(x)) g’(x) = 1.  

Let g(1) = K, then (g(1)) = 1 f(k) = 1. Since (0) = 1 and is continuous and increasing function so one-one thus k = 0. Putting x = 1 in (i), we getf’(0) g’(1) = 1. But f’(x) = 3x2 + (1/2) ex/2 ⇒ f’(0) = 1/2  

SIMILAR QUESTIONS

Q1
Q3

 for real and y. If f’(0) exists and equals – 1 and (0) = 1 then the value of f(2) is

Q4

If f : R  R is a function such that (x) = x3 + x2 f’(1) + xf’’(2) + f’’’(3) for x Ïµ R then the value of f (2) is

Q5

 and n are integers, m ≠ 0, n > 0, and let p be the left hand derivative of |x – 1| at x = 1. If 

Q6

If f (x) = |x – 2| and g(x) = f (f (x)), then for x > 20, g’(x) is equal to

Q7

If f (9) = 9 and f’(9) = 4, then 

Q8

The derivatives of sec –1 [1/(2x2 – 1)] with respect to  at x = ½, is

Q9

Let F(x) = f(xg(xh(x) for all real x, where f(x), g(x) and h(x) are differentiable functions. At some point x0,