Home
Class 12
MATHS
Let f: R-{3/5}->R be defined by f(x)=(3x...

Let `f: R-{3/5}->R` be defined by `f(x)=(3x+2)/(5x-3)` . Then

Text Solution

Verified by Experts

Given that,
`f(x)=(3x+2)/(5x-3)`
let `y=(3x+2)/(5x-3)`
`=>3x+2=5xy−3y`
`=>x(3−5y)=−3y−2`
`=>f^-1(x)=(3x+2)/(5x-3)`
`therefore f ^(−1)(x)=f(x) `
Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

Similar Questions

Explore conceptually related problems

Let f:R-{(3)/(5)}rarr R be defined by f(x)=(3x+2)/(5x-3). Then

If f" R -{3/5} to R be defined by f(x)=(3x+2)/(5x-3) , then :

Let f: R-{-3/5}->R be a function defined as f(x)=(2x)/(5x+3) . Write f^(-1) : Range of f->R-{-3/5} .

Let f: R -{3} to R-{1} be defined by f(x) =(x-2)/(x-3) Let g: R to R be given as g(x)=2x-3. Then, the sum of all the values of x for which f^(-1) (x)+g^(-1) (x)=(13)/2 is equal to

Let f: R to R be defined by f(x) = 5^(2x)/(5^(2x) + 5) , then f(x) + f(1-x) is equal to

f:R rarr R defined by f(x)=x^(2)+5

Let f: R to R be defined by f(x) = (3x^(2)+3x-4)/(3-3x + 4x^(2)) , then

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then f(x)=sin^2x ,g(x)...

    Text Solution

    |

  2. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  3. If the function f:(1,)vec(1,oo) is defined by f(x)=2^(x(x-1)),t h e nf...

    Text Solution

    |

  4. Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=x for all x in R (b) ...

    Text Solution

    |

  5. If the function f: R->R be such that f(x) = x-[x], where [x] denotes t...

    Text Solution

    |

  6. If F :[1,oo)vec[2,oo) is given by f(x)=x+1/x ,t h e nf^(-1)(x) equals....

    Text Solution

    |

  7. Let g(x)=1+x-[x]a n df(x)={-1, x<0 0, x=0f, x >0 . Then for all x ,f(g...

    Text Solution

    |

  8. Let f(x)=(alphax)/((x+1)),x!=-1. The for what value of alpha is f(f(x)...

    Text Solution

    |

  9. If f :[2,oo)rarr(-oo,4], where f(x)=x(4-x) then find f^-1(x)

    Text Solution

    |

  10. If f: Rvec(-1,1) is defined by f(x)=-(x|x|)/(1+x^2),t h e nf^(-1)(x) e...

    Text Solution

    |

  11. If g(x)=x^2+x-2a n d1/2gof(x)=2x^2-5x+2, then which is not a possible ...

    Text Solution

    |

  12. If f(x)=sin^2x and the composite function g(f(x))=|sinx| , then g(x)...

    Text Solution

    |

  13. Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3...

    Text Solution

    |

  14. Let f(x)=x^3 be a function with domain {0, 1, 2, 3}. Then domain of...

    Text Solution

    |

  15. Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3...

    Text Solution

    |

  16. Let f: R->R be given by f(x)=tanx . Then, f^(-1)(1) is pi/4 (b) {npi+p...

    Text Solution

    |

  17. Let A={1,2,..., n} and B={a , b }. Then number of subjections from A i...

    Text Solution

    |

  18. If the set A contains 5 elements and the set B contains 6 elements, th...

    Text Solution

    |

  19. If the set A contains 7 elements and the set B contains 10 elements, ...

    Text Solution

    |

  20. Let f: R-{3/5}->R be defined by f(x)=(3x+2)/(5x-3) . Then

    Text Solution

    |