Home
Class 12
MATHS
Let f:[-1,\ oo)->[-1,\ oo) is given by f...

Let `f:[-1,\ oo)->[-1,\ oo)` is given by `f(x)=(x+1)^2-1` , `xgeq-1` . Show that `f` is invertible. Also, find the set `S={x ,\ f(x)=f^(-1)(x)}` .

A

`{0,-1,(-3pm sqrt(3))/(2)}`

B

{0,1,-1}

C

{0,-1}

D

{}

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.1|8 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 1.2|12 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 1d|10 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f is invertible. Also, find the set S={x :f(x)=f^(-1)(x)}dot

Let f:[-1,oo]vec[-1,) is given by f(x)=(x+1)^2-1,xgeq-1. Show that f is invertible. Also, find the set S={x :f(x)=f^(-1)(x)}dot

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

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)

Let f: R-{-1}->R-{1} be given by f(x)=x/(x+1) . Write f^(-1)(x) .

Let f: R->R be defined by f(x)=3x-7 . Show that f is invertible and hence find f^(-1) .

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

Let f:[-1,oo] in [-1,oo] be a function given f(x)=(x+1)^(2)-1, x ge -1 Statement-1: The set [x:f(x)=f^(-1)(x)]={0,1} Statement-2: f is a bijection.

Show that f: R-{-1}->R-{1} given by f(x)=x/(x+1) is invertible. Also, find f^(-1) .

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.