Home
Class 12
MATHS
Let f: NvecR be a function defined as f(...

Let `f: NvecR` be a function defined as `f(x)=4x^2+12 x+15.` Show that `f: NvecS ,` where `S` is the range of `f,` is invertible. Also find the inverse of `f`

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos

  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

Let f: N -> R be a function defined as f(x)=4x^2+12 x+15. Show that f: N -> S, where S is the range of f is invertible. Also find the inverse of f

Let f : N ->R be a function defined as f(x)=4x^2+12 x+15 . Show that f : N-> S , where, S is the range of f, is invertible. Find the inverse of f.

Let f: Nvec be a function defined as f(x)=9x^2+6x-5. Show that f: NvecS , where S is the range of f, is invertible. Find the inverse of f and hence f^(-1)(43) and f^(-1)(163)dot

Let f: N -> S be a function defined as f(x)=9x^2+6x-5 . Show that f:N -> S, where S is the range of f , is invertible. Find the inverse of f and hence f^(-1)(43) and f^(-1)(163)

Let f: N->Z be a function defined as f(x)=x-1000. Show that f is an into function.

If f: RvecR be the function defined by f(x)=4x^3+7, show that f is a bijection.

Let f:R rarr R be a function defined as f(x)=(x^(2)-6)/(x^(2)+2) , then f is

If f: R->R be the function defined by f(x)=4x^3+7, show that f is a bijection.

If f: R->R be the function defined by f(x)=4x^3+7 , show that f is a bijection.

Let f:[-1,1] to R_(f) be a function defined by f(x)=(x)/(x+2) . Show that f is invertible.

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. int0^(pi/2)frac{2^sinx}{2^sinx+2^cosx}dx

    Text Solution

    |

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

    Text Solution

    |

  3. Let f: NvecR be a function defined as f(x)=4x^2+12 x+15. Show that f: ...

    Text Solution

    |

  4. Let A=R-{3} and B=R-[1]dot Consider the function f: AvecB defined by f...

    Text Solution

    |

  5. Let f,g:vec R be defined by f(x)=2x+1 and g(x)=x^2-2 for all x in R, r...

    Text Solution

    |

  6. Let A and B be any two sets such that n(B)=P, n(A)=q then the total nu...

    Text Solution

    |

  7. If f: A->A ,g: A->A are two bijections, then prove that (i) fog is an ...

    Text Solution

    |

  8. Let f: Z->Z be defined by f(x)=x+2. Find g: Z->Z such that gof=IZ .

    Text Solution

    |

  9. Which one the following relations on A={1,2,3} is function? f={(1,3),(...

    Text Solution

    |

  10. Write the domain of the real function f defined by f(x)=sqrt(25-x^2) .

    Text Solution

    |

  11. Let A}x :-1lt=xlt=1}a n df: Avec A such that f(x)=x|x|, then f is (a) ...

    Text Solution

    |

  12. If the function f:[1,oo)rarr[1,oo) is defined by f(x)=2^(x(x-1)),t h e...

    Text Solution

    |

  13. If f(x)=(x-1)/(x+1),x!=-1, then show that f(f(x))=-1/x provided that x...

    Text Solution

    |

  14. Let f be a real function defined by f(x)=sqrt(x-1.) Find (fofof)(x)dot...

    Text Solution

    |

  15. Let f: R-> R be the function defined by f(x)=4x−3 for all x in R. Then...

    Text Solution

    |

  16. Find whether f: R->R given by f(x)=x^3+2 for all x in R .

    Text Solution

    |

  17. Find whether f: Z->Z given by f(x)=x^2+1 for all x in Z

    Text Solution

    |

  18. Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , i...

    Text Solution

    |

  19. Discuss the surjectivity of f: R->R given by f(x)=x^3+2 for all x i...

    Text Solution

    |

  20. Discuss the surjectivity of f: R->R given by f(x)=x^2+2 for all x i...

    Text Solution

    |