Let g be a real valued function defined ...

Let g be a real valued function defined on the interval (-1, 1) such that `e^(-x) (g (x) - 2e^(x)) = underset(0)overset(x)intsqrt(y^(4) +1) dy` for all ` in (-1, 1)` and f be an another function such f(g(x)) = g(f(x)) = x. Then the value of f'(2) is

`(1)/(2)`

`(1)/(4)`

`(1)/(5)`

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

RELATIONS AND FUNCTIONS
AAKASH INSTITUTE|Exercise Assignment (Section - C) Objective Type Questions (More than one option are correct)|17 Videos
RELATIONS AND FUNCTIONS
AAKASH INSTITUTE|Exercise Assignment (Section - D) Linked Comprehension Type Questions|17 Videos
RELATIONS AND FUNCTIONS
AAKASH INSTITUTE|Exercise Assignment (Section - A) Objective Type Questions (one option is correct)|102 Videos
PROBABILITY
AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|13 Videos
SEQUENCES AND SERIES
AAKASH INSTITUTE|Exercise Assignment (SECTION - J) Aakash Challengers|12 Videos

Similar Questions

Explore conceptually related problems

Let f be a real-valued function on the interval (-1,1) such that e^(-x) f(x)=2+underset(0)overset(x)int sqrt(t^(4)+1), dt, AA x in (-1,1) and let f^(-1) be the inverse function of f. Then [f^(-1) (2)] is a equal to:

If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x) , then the value of g'(1) is

g(x) is a inverse function of f.g(x)=x^(3)+e^((x)/(2)) then find the value of f'(x)

If the function _(x)f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x), then the value of g'(1) is

Let f and g be two real valued functions ,defined by f(x) =x ,g(x)=[x]. Then find the value of f+g

If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x) , then the value of g'(x) is

If the functions f(x)=x^(5)+e^(x//3) " and " g(x)=f^(-1)(x) , the value of g'(1) is ………… .

AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)

Range ofthe function f(x)=cos(Ksin x) is [-1,1], then the least positi...
Text Solution
|
Consider that the graph of y = f(x) is symmetrie about the lines x =...
Text Solution
|
Let f(x) be defined in (0, 1), then the domain of definition of f(e^...
Text Solution
|
If f(x) = 4^(x) - 2^(x + 1) + 5, then range of f(x) is
Text Solution
|
Let g be a real valued function defined on the interval (-1, 1) such t...
Text Solution
|
If f(x) is a real valued function defined as f(x) = In(1 - sin x) then...
Text Solution
|
if f(x) is a real valued function defined as f(x)={min{|x|,1/x^2,1/x^3...
Text Solution
|
Select the correct option
Text Solution
|
Let f(x) = [x]^(2) + [x+1] - 3, where [.] denotes the greatest integer...
Text Solution
|
If 2^(f(x)) = (2+x)/(2-x), x in (-2, 2) and f(x) = lambda f((8x)/(4+ x...
Text Solution
|
If tan ax + cot ax and |tan x| + |cot x| are periodic functions of th...
Text Solution
|
If {x} and [x] represent fractional and integral part of x, then [x]+...
Text Solution
|
Let g(x) = x - [x] - 1 and f(x) = {{:(-1", " x lt 0),(0", "x =0),(1",...
Text Solution
|
If the function f(x) = [4.8 + asinx] (where [.]- * denotes the greates...
Text Solution
|
[(4)/(5)] + [(4)/(5)+(1)/(1000)] + [(4)/(5)+(2)/(1000)] + ...+[(4)/(5)...
Text Solution
|
A real valued function f(x) satisfies the functional equation f(x-y) ...
Text Solution
|
lf f: R rarr R satisfies, f(x + y) = f(x) + f(y), AA x, y in R and f(1...
Text Solution
|
Let f: RvecRa n dg: RvecR be two one-one and onto function such that t...
Text Solution
|
If f(x+10) + f(x+4), there f(x) is a periodic function with period
Text Solution
|
If f(x) = a(x^n +3), f(1) = 12, f(3) = 36, then f(2) is equal to
Text Solution
|