Home
Class 12
MATHS
Let RR be the set of real numbers and f:...

Let `RR` be the set of real numbers and `f:RR rarr RR ` be given by `f(x)=x^(2) +2`. Find
(i)`f^(-1){11,16}` (ii) `f^(-1) {11 le x le 27}`
`(iii) f^(-1) {0 le x le 6}` (iv) `f^(-1) {-2 le xle 2}`
(v) `f^(-1) {- infty lt x le 4}`

Text Solution

Verified by Experts

The correct Answer is:
(i) `={3,-3, sqrt14,-sqrt14}` (ii) `={x:-5 le x le -3 or, 3le x le 5}` (iii) `f^(-1){0 le x le 6} = {x:- 2 le x le 2}` (iv) `f^(-1){-2 le x le 2} = {0} ` (v) `f^(-1) { -infty lt x le 4}={x:-sqrt2 le x le sqrt2}`
Promotional Banner

Topper's Solved these Questions

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|12 Videos

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( very short answer type questions)|22 Videos

  • LOGARITHM

    CHHAYA PUBLICATION|Exercise Long Answer Type Question|12 Videos

  • MATHEMATICAL REASONING

    CHHAYA PUBLICATION|Exercise JEE Main (AIEEE) Archive (2016 )|1 Videos

Similar Questions

Explore conceptually related problems

Let RR be the set of real numbers and f: RR rarr RR be defined by , f(x) =x^(3) +1 , find f^(-1)(x)

Let the function f: RR rarr RR be defined by f(x)=x^(2)-2 . Find (i) f^(-1) {-1,7} ,(ii) f^(-1) {2 le xle 34} , (iii) f^(-1) {-5 le xle 14} (iv) f^(-1){-6 le xle -2} ,(v) f^(-1) { - infty lt x le 2} .

Let RR be the set of real numbers and f:RR rarr RR be defined by , f(x)=2x^(2)-5x+6 .Find f^(-1)(5) and f^(-1)(2)

Let RR be the set of real number and f: RR rarr RR , be given by f(x)=2x^(2)-1 . .Is this mapping one -one ?

Let RR be the set of real numbers and the mapping f: RR rarr RR be defined by f(x)=2x^(2) , then f^(-1) (32)=

Let RR be the set of all real numbers and f : R to R be given by f(x) = 3 x^(2) +1 then the set f^(-1) ([1,6]) is -

Let RR be the set of real numbers and f:RR to RR be given by, f(x)=log_ex. Does f define a function ?

Let the function f: RR rarr RR be given by , f(x)=3x^(2)-14x+10 . Find (i) f^(-1)(4), (ii) f^(-1) (-8)

Let RR be the set of real numbers and f : RR to RR be defined by f(x)=sin x, then the range of f(x) is-

Let R be the set of real numbers and f:R to R be defined by f(x)=x^(2)+2 , then the set f^(-1)(11 le x le 27) is -