Home
Class 11
MATHS
If f(x)=log((1-x)/(1+x)), show that f(a)...

If `f(x)=log((1-x)/(1+x))`, show that `f(a)+f(b)=f((a+b)/(1+ab))`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    ICSE|Exercise EXERCISE 2 (f)|29 Videos
  • RELATIONS AND FUNCTIONS

    ICSE|Exercise EXERCISE 2 (g)|37 Videos
  • RELATIONS AND FUNCTIONS

    ICSE|Exercise EXERCISE 2 (d)|18 Videos
  • RELATION AND FUNCTIONS

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS (Choose the correct answer from the given four options in questions)|32 Videos
  • SAMPLE QUESTION PAPER 01

    ICSE|Exercise SECTION C|8 Videos

Similar Questions

Explore conceptually related problems

If f(x)=log_e((1-x)/(1+x)); prove that f(a)+f(b)=f((a+b)/(1+a b))

If f.(x)= log((1+x)/(1-x)) , then

If f(x)=(x+1)/(x-1) , show that f{f(x)}=xdot

If f(x)=1/(1-x) , show that f[f{f(x)}]=xdot

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=x^3-1/(x^3) , show that f(x)+f(1/x)=0.

If f(x)=(4^(x))/(4^(x)+2) , then show that f(x)+f(1-x)=1

If f(x)=(x-1)/(x+1) , then prove that: (f(b)-f(a))/(1+f(b)*f(a))=(b-a)/(1+ab)

Let f(x) = ln ((1-sinx)/(1+sinx)) , then show that int_(a)^(b) f(x)dx = int_(b)^(a) ln((1+sinx)/(1-sinx))dx .

If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^2)]=2f(x)dot