Home
Class 12
MATHS
Let f and g be differentiable functions ...

Let `f` and `g` be differentiable functions such that: `xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R` Also, `f(x)gt0` and `g(x)gt0 AA x in R` `int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R` and `g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R` Now answer the question: `f(g(0))+g(f(0))=` (A) `1` (B) `2` (C) `3` (D) `4`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    VK JAISWAL|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|2 Videos

  • DIFFERENTIAL EQUATIONS

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|6 Videos

  • DIFFERENTIAL EQUATIONS

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|6 Videos

  • DETERMINANTS

    VK JAISWAL|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|11 Videos

  • ELLIPSE

    VK JAISWAL|Exercise Exercise-4 : Subjective Type Problems|2 Videos

Similar Questions

Explore conceptually related problems

Suppose f and g are differentiabel functions such that xg (f(x))f'(g (x))g '(x) =(g(x))g '(f(x)) f'(x) AA x in R and f is positive AA n in R. Also int _( 0)^(x) f (g(t )) dt =1/2 (1-e^(-2x))AA x in R, g (f(0))=1 and h (x) = (g(f (x)))/(f (g(x)))AA x in R. The largest possible value of h(x)AA x in R is:

Suppose f and g are differentiabel functions such that xg (f(x))f'(g (x))g '(x) =(g(x))g '(f(x)) f'(x) AA x in R and f is positive AA n in R. Also int _( 0)^(x) f (g(t )) dt =1/2 (1-e^(-2x))AA x in R, g (f(0))=1 and h (x) = (g(f (x)))/(f (g(x)))AA x in R. The graph of y =h (x) is symmetric with respect to line:

Let g'(x)gt 0 and f'(x) lt 0 AA x in R , then

Let g'(x)>0 and f'(x)<0AA x in R, then

f and g differentiable functions of x such that f(g(x))=x," If "g'(a)ne0" and "g(a)=b," then "f'(b)=

If f and g are derivable function of x such that g'(a)ne0,g(a)=b" and "f(g(x))=x," then 'f'(b)=

f(x)=x^(2)-2x,x in R, and g(x)=f(f(x)-1)+f(5-f(x)) Show that g(x)>=0AA x in R

f(x) and g(x) are two differentiable functions in [0,2] such that f(x)=g(x)=0,f'(1)=2,g'(1)=4,f(2)=3,g(2)=9 then f(x)-g(x) at x=(3)/(2) is

f(x) and g(x) are two differentiable functions in [0,2] such that f(x)=g(x)=0,f'(1)=2,g'(1)=4,f(2)=3,g(2)=9 then f(x)-g(x) at x=(3)/(2) is