Home
Class 12
MATHS
Find all possible values of expressions ...

Find all possible values of expressions `(2+x^2)/(4-x^2)`

Text Solution

Verified by Experts

The correct Answer is:
`(-oo , -1) cup [1/2 ,oo)`
`(2+x^2)/(4 -x^2)=((6-(4-x^2))/(4-x^2)=(6)/(4-x^2)-1`
Now `x^2 ge 0 `
`therefore -x^2 le 0`
`rArr 4-x^2 le 4 `
`rArr (4-x^2)/(6) le 2/3`
`rArr -oo lt (4-x^2)/(6) lt 0 or 0 lt (4-x^2)/(6) le 2/3 `
`rArr 0 gt (6)/(4-x^2) gt -oo of oo gt (6)/(4-x^2) ge 3/2`
`rArr (6)/(4-x^2) in (-oo , 0 ) cup [3/2 , oo)`
`rArr ((6)/(4-x^2)-1)in(-oo , -1) cup [1/2 , oo)`
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.3|13 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.4|11 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.1|12 Videos

  • SEQUENCE AND SERIES

    CENGAGE|Exercise Question Bank|1 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|3 Videos

Similar Questions

Explore conceptually related problems

Find all the possible values of following expressions : (i) ( |x|)/(x) + (|y|)/y (ii) |x|/x+|y|/y+|z|/z

Find all the possible values of f(x) =(1-x^2)/(x^2+3)

Find all possible values of (x^2+1)/(x^2-2) .

Find all the possible values of the following expressions: 1/(x^2+2) (ii) 1/(x^2-2x+3) (iii) 1/(x^2-x-1)

Let x,y in R , then find the maximum and minimum values of expression (x^(2)+y^(2))/(x^(2)+xy+4y^(2)) .

For x in R , find all possible values of |x-3|-2 (ii) 4-|2x+3|

Find the possible values of sin^(-1) (1 - x) + cos^(-1) sqrt(x -2)

If x is real, then the value of the expression (x^2+14x+9)/(x^2+2x+3) lies between (a) 5 and 4 (b) 5 and -4 (c) -5 and 4 (d) none of these

Find all the possible the value of the following expression dot sqrt(x^2-4) (ii) sqrt(9-x^2) (iii) sqrt(x^2-2x+10)