Home
Class 12
MATHS
Consider f:R(+) [4, oo] is given by f(x)...

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

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MODERN PUBLICATION|Exercise PROBLEM|18 Videos

  • SAMPLE PAPER 2012

    MODERN PUBLICATION|Exercise EXERCISE|37 Videos

Similar Questions

Explore conceptually related problems

Consider f:R_(+) to [-5, oo) given by f(x)=9x^(2)+6x-5 . Show that f is invertible with f^(-1)(y)= ((sqrt(y+6)-1)/(3)) . Hence. Find (i) f^(-1)(10)" " (ii) y" if "f^(-1)(y)=(4)/(3) where R_(+) is the set of all non-negative real numbers.

Consider f : R rarr (-9 ,oo) given by f(x) = 5x^(2)+ 6x-9 . Prove that f is invertible with f^(-1) (y) = ((sqrt(54+5y)-3)/(5)) where R^(+) is the set of all positive real numbers.

Let Y = { n^(2)n in N}sub N. Consider f:N rarr Y as f(n) = n^(2) . Show that f is invertible. Also, find the inverse of f.

Consider f:R -{-(4)/(3)} to R -{(4)/(3)} given by f(x) =(4x+3)/(3x+4) . Show that f is bijective. Find the inverse of f and hence find f^(-1)(0) and x such that f^(-1)(x)=2 .

Show that f:R to R defined as f(x)= 4x+3 is invertible. Find the inverse of 'f' .

MODERN PUBLICATION-RELATION AND FUNCTIONS-EXERCISE
  1. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

    Text Solution

    |

  2. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

    Text Solution

    |

  3. Let * is a binary operation on the set of all non-zero real numbers, g...

    Text Solution

    |

  4. Test whether the relations are reflexive, symmetric or transitive on t...

    Text Solution

    |

  5. Suppose a box contains a set of n balls (n gt 4)(denoted by B )of four...

    Text Solution

    |

  6. If f:XtoY and g:YtoZ be two bijective functions, then prove that (gof)...

    Text Solution

    |

  7. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

    Text Solution

    |

  8. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

    Text Solution

    |

  9. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

    Text Solution

    |

  10. Examine f:(-1,1) rarr R,f(x) = x/(1-x^2functions if it is (i) injecti...

    Text Solution

    |

  11. Consider f:R(+) [4, oo] is given by f(x)= x^(2) + 4. Show that f is in...

    Text Solution

    |

  12. Test whether the relations are reflexive, symmetric or transitive on t...

    Text Solution

    |

  13. Find the number of equivalence, relations on X ={1,2,3),

    Text Solution

    |

  14. Let A = {1, 2, 3). Then, show that the number of relations containing ...

    Text Solution

    |

  15. Let R be a relation on the set A of ordered pairs of positive integers...

    Text Solution

    |

  16. Show that f : N to N, given by f(x)= {(x+1", if x is odd"),(x-1", if...

    Text Solution

    |

  17. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

    Text Solution

    |

  18. Congruence modulo 3 relation partitions the set Z into how many equiva...

    Text Solution

    |

  19. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  20. Constract the composition table/multiplication table for the binary op...

    Text Solution

    |