Home
Class 12
MATHS
If f: R^+vecR ,f(x)+3xf(1/x)=2(x+1) then...

If `f: R^+vecR ,f(x)+3xf(1/x)=2(x+1) then f(x)` is

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=(x+1)//2`
`f(x)+3x f((1)/(x))=2(x+1) " (1)" `
Replacing `x` by `(1)/(x),` we get
`f((1)/(x))+3(1)/(x)f(x)=2((1)/(x)+1)`
or ` x f((1)/(x))+3f(x)=2(x+1) " (2)" `
From (1) and (2), we have `f(x)=(x+1)/(2).`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.15|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|125 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.13|7 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

If f : R - {1} rarr R, f(x) = (x-3)/(x+1) , then f^(-1) (x) equals

Let f : R to and f (x) = (x (x^(4) + 1) (x+1) +x ^(4)+2)/(x^(2) +x+1), then f (x) is :

Consider the function f:R -{1} given by f (x)= (2x)/(x-1) Then f^(-1)(x) =

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

If f(x)+2f(1-x)=x^2+2AA x in R, then f(x) given as

Let f(x) = x - [x] , x in R then f(1/2) is

If f:R-{-(1)/(2)}toR-{(1)/(2)} is defined by f(x)=(x-3)/(2x+1) , then f^(-1)(x) is

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :