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

  • TEST PAPER 5

    MODERN PUBLICATION|Exercise PROBLEM|41 Videos
  • TEST PAPER 7

    MODERN PUBLICATION|Exercise EXERCISE|39 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-TEST PAPER 6-EXERCISE
  1. Find the volume of parallelopiped with edges 2vec i-3vec j ,vec i +vec...

    Text Solution

    |

  2. Show that the relation R on the set A = {1,2,3,4,5) given by R = {(a,b...

    Text Solution

    |

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

    Text Solution

    |

  4. A merchant sells two models X and Y of TV with cost price ₹ 25000 and ...

    Text Solution

    |

  5. A binary operation * is defined on the set X=R-{-1} by x**y=x+y +xy,...

    Text Solution

    |

  6. Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4ab

    Text Solution

    |

  7. Using determinants, find the values of a if the area of triangle with ...

    Text Solution

    |

  8. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

    Text Solution

    |

  9. Using properties of determinant prove that |{:(alpha,beta,gamma),(alph...

    Text Solution

    |

  10. Differentiate tan^-1((2x)/(1-x^2)).

    Text Solution

    |

  11. Examine continuity and differentiability f(x)={[xsin1/x,if x!=0],[0,if...

    Text Solution

    |

  12. Find dy/dx if y=(cosx)^x.

    Text Solution

    |

  13. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

    Text Solution

    |

  14. Find the interval where y=sin2x-cos2x,xin[0,2pi] is (a) incresing (b)...

    Text Solution

    |

  15. Evaluate:int (sin x-xcosx)/(x(x+sinx)) dx.

    Text Solution

    |

  16. Integrate : int sin^(-1)xdx.

    Text Solution

    |

  17. Find the particular solution of d^2 y/dx^2 =2x,given that x=0,y=2 and ...

    Text Solution

    |

  18. Solve :-(x^2+y^2)dx-2xy dy=0

    Text Solution

    |

  19. If with reference to the eight handed system of mutually perpendicular...

    Text Solution

    |

  20. If vec a =(2,3,6), vec b=(2,-2,1), vec c=(-1,0,2), find the direction ...

    Text Solution

    |