Home
Class 12
MATHS
If f: R->R defined by f(x)=3x-4 is inver...

If `f: R->R` defined by `f(x)=3x-4` is invertible then write `f^(-1)(x)` .

Text Solution

Verified by Experts

Let `f^{-1}(x)=y`

`Rightarrow {f}({y})={x}`

It is given that, `f(x)=3 x-4`, then `f(y)=3 y-4`

`Rightarrow 3 y-4=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

If f:R rarr R defined by f(x)=(2x-1)/(5) be an invertible function, write f^(-1)(x) .

Prove that the function f: R->R defined as f(x)=2x-3 is invertible. Also, find f^(-1) .

If f: R to R is defined as f(x)=2x+5 and it is invertible , then f^(-1) (x) is

f:R rarr R defined by f(x)=x^(3)-4

If f: R->R is defined by f(x)=10 x-7 , then write f^(-1)(x) .

Let f: R->R be defined by f(x)=3x-7 . Show that f is invertible and hence find f^(-1) .

If f: Rrarr R defined by f(x) = 3x+2a cos x -5 is invertible then 'a' belongs to

(a) If f:RrarrR defined by f(x)=(3x+5)/(2) is an invertible function, find f^(-1) . Show that f:RrarrR defined by f(x)=(4x-3)/(5),x inR is invertible function and find f^(-1) .

If f: R->R is defined by f(x)=3x+2 , find f(f(x)) .

If f:R to R is defined by f(x)=|x|, then

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. If f: R->R is defined by f(x)=10 x-7 , then write f^(-1)(x) .

    Text Solution

    |

  2. Let f:{-pi/2,\ pi/2}->R be a function defined by f(x)=cos[x]dot Write ...

    Text Solution

    |

  3. If f: R->R defined by f(x)=3x-4 is invertible then write f^(-1)(x) .

    Text Solution

    |

  4. If f: R->R , g: R->R are given by f(x)=(x+1)^2 and g(x)=x^2+1 , then w...

    Text Solution

    |

  5. Let A={x in R :-4lt=xlt=4 and x!=0} and f: A->R be defined by f(x)=(|...

    Text Solution

    |

  6. Let f:[-pi/2,\ pi/2]->A be defined by f(x)=sinx . If f is a bijection,...

    Text Solution

    |

  7. Let f: R->R^+ be defined by f(x)=a^x ,\ a >0 and a!=1 . Write f^(-1)(x...

    Text Solution

    |

  8. Let f: R-{-1}->R-{1} be given by f(x)=x/(x+1) . Write f^(-1)(x) .

    Text Solution

    |

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

    Text Solution

    |

  10. Let f: R->R , g: R->R be two functions defined by f(x)=x^2+x+1 and g(x...

    Text Solution

    |

  11. Let f: R->R be defined as f(x)=(2x-3)/4 . Write fof^(-1)(1) .

    Text Solution

    |

  12. Let f be an invertible real function. Write (f^(-1)\ of)(1)+(f^(-1)...

    Text Solution

    |

  13. Let A={1,\ 2,\ 3,\ 4} and B={a ,\ b} be two sets. Write total numbe...

    Text Solution

    |

  14. Write the domain of the real function f(x)=sqrt(x-[x]) .

    Text Solution

    |

  15. Write the domain and range of function f(x) given by f(x)=sqrt([x]-x)d...

    Text Solution

    |

  16. Write the domain of the real function f(x)=1/(sqrt(|x|-x))

    Text Solution

    |

  17. Write whether f: R->R given by f(x)=x+sqrt(x^2) is one-one, many-one, ...

    Text Solution

    |

  18. If "f"("x")=x+7 and g(x)=x-7,\ x\ \ R , find (fog)(7)

    Text Solution

    |

  19. What is the range of the function f(x)=[|x-1|]/[x-1]

    Text Solution

    |

  20. If f\ : R-: R be defined by f(x)=(3-x^3)^(1//3)\ , then find fof(x)

    Text Solution

    |