Home
Class 12
MATHS
A function f: R->R is defined as f(x)=x^...

A function `f: R->R` is defined as `f(x)=x^3+4` . Is it a bijection or not? In case it is a bijection, find `f^(-1)(3)` .

Text Solution

Verified by Experts

Let x and y be two elements of domain (R),
Such that f(x)=f(y)
`Rightarrow x^3+4=y^3+4 `
` Rightarrow x^3=y^3 `
` Rightarrow x=y`
Therefore, f is one-one.
...
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

the function f:R rarr R defined as f(x)=x^(3) is

The function f:R rarr R defined as f(x) = x^3 is:

If a function f: R to R is defined as f(x)=x^(3)+1 , then f is

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

The function f: R to R defined by f(x) = 4x + 7 is

The function f:R rarr R is defined by f(x)=3^(-x)

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

If a funciton f:[2,oo] to B defined by f(x)=x^(2)-4x+5 is a bijection, then B=

Show that f:R rarr R, defined as f(x)=x^(3) is a bijection.

Show that the function f:R rarr R given by f(x)=x^(3)+x is a bijection.

RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. Consider f: R+->[-5,oo)given by f(x)=9x^2+6x-5. Show that f is inverti...

    Text Solution

    |

  2. If f: R->R be defined by f(x)=x^3-3 , then prove that f^(-1) exists an...

    Text Solution

    |

  3. A function f: R->R is defined as f(x)=x^3+4 . Is it a bijection or not...

    Text Solution

    |

  4. If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=...

    Text Solution

    |

  5. Let A=R-{3}a n dB=R-{1}dot Consider the function f: Avec defined by f(...

    Text Solution

    |

  6. Consider f:R+->[-9,oo[ given by f(x)=5x^2+6x-9. Prove that f is invert...

    Text Solution

    |

  7. Let f: Nvec be a function defined as f(x)=9x^2+6x-5. Show that f: Nvec...

    Text Solution

    |

  8. If f: Rvec(-1,1) defined by f(x)=(10^x-10^(-x))/(10^x+10^(-x)) is inve...

    Text Solution

    |

  9. If f: R->(0,\ 2) defined by f(x)=(e^x-e^(-x))/(e^x+e^(-x))+1 is invert...

    Text Solution

    |

  10. Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f i...

    Text Solution

    |

  11. Let A={x in R|-1lt=xlt=1} and let f: A->A ,\ g: A->A be two functions...

    Text Solution

    |

  12. Let f be a function from R to R such that f(x)=cos(x+2) . Is f inverti...

    Text Solution

    |

  13. If A={1,\ 2,\ 3,\ 4} and B={a ,\ b ,\ c ,\ d} . Define any four bij...

    Text Solution

    |

  14. Let A and B be two sets each with a finite number of elements. Assume ...

    Text Solution

    |

  15. If f: AvecA ,g: Avec are two bijections, then prove that fog is an inj...

    Text Solution

    |

  16. If f: A->A ,\ \ g: A->A are two bijections, then prove that fog is an ...

    Text Solution

    |

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

    Text Solution

    |

  18. Write total number of one-one functions from set A={1,\ 2,\ 3,\ 4} ...

    Text Solution

    |

  19. If f: R->R is defined by f(x)=x^2 , write f^(-1)(25) .

    Text Solution

    |

  20. If f: C->C is defined by f(x)=x^2 , write f^(-1)(-4) . Here, C denotes...

    Text Solution

    |