Home
Class 12
MATHS
Consider f:R+->[-9,oo[ given by f(x)=5x^...

Consider `f:R_+->[-9,oo[` given by `f(x)=5x^2+6x-9`. Prove that `f` is invertible with `f^(-1)(y)=(sqrt(54+5y)-3)/5`

Text Solution

AI Generated Solution

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

Consider f: R_+->[-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=(((sqrt(y+6))-1)/3)

Consider f: R rarr [-5,oo) given by f(x)=9x^2+6x-5 . Show that f is invertible with f^(-1)(y)=((sqrt(y+6)-1)/3)dot

Consider f: R->R given by f(x) = 4x + 3 . Show that f is invertible. Find the inverse of f.

Consider f: R->R given by f(x) = 4x + 3 . Show that f is invertible. Find the inverse of f .

Consider f\ : R_+vec[4,oo) given by f(x)=x^2+4 . Show that f is invertible with the inverse f^(-1) of f given by f^(-1)(y)=sqrt(y-4),\ where R_+ is the set of all non-negative real numbers.

f:R to R given by f(x)=5-3 sin x, is

Consider f: R^+ rarr [4, oo] given by f(x)=x^2+4. Show that f is invertible with the inverse (f^(-1)) of f given by f^(-1)\ (y)=sqrt(y-4) , where R^+ is the set of all non-negative real numbers.

For the function f given by f(x)=x^2-6x+8 , prove that f\ '\ (5)=4 .

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

if the function f: R rarr R given be f(x)=x^3 + ax^2 + 5 x + sin 2x is invertible then

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. If f: Q->Q ,\ \ g: Q->Q are two functions defined by f(x)=2x and g(x)=...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Which one of the following graphs represent a function? (FIGURE)

    Text Solution

    |

  15. Which one of the following graphs represent a one-one function? (FI...

    Text Solution

    |

  16. Let A={1,\ 2} and B={a ,\ b} be two sets. Write total number of one-...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. If f: R->R is given by f(x)=x^3 , write f^(-1)(1) .

    Text Solution

    |