Home
Class 12
MATHS
If A={x:x^(2)-2x+2gt0}andB={x:x^(2)-4x+3...

If `A={x:x^(2)-2x+2gt0}andB={x:x^(2)-4x+3le0}`
`AuuB` equals

A

`(-oo,1)`

B

`(3,oo)`

C

`(-oo,oo)`

D

(1,3)

Text Solution

Verified by Experts

The correct Answer is:
C
`A={x:x^(2)-2x+2gt0}={x:(x-1)^(2)+1gt0}=(-oo,oo)`
`B={x:x^(2)-4x+3le0}={x:(x-1)(x-3)le0}`
`={x:1lexle3}=[1,3]`
`AuuB=(-oo,oo)uu[1,3]=(-oo,oo)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A={x:x^(2)-2x+2gt0}andB={x:x^(2)-4x+3le0} AnnB equals

If A={x:x^(2)-2x+2gt0}andB={x:x^(2)-4x+3le0} A - B equals

If A=[{:(0,1,2),(2,-3,0),(1,-1,0):}]andf(x)=x^(3)+4x^(2)-x , then find f(A).

The area of the region bounded by {(x,y) : y^2 ge 2x and x^2 +y^2 le 4x , x ge 0 , y ge 0} is ….Sq. units.

If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =3 then the value of |{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| is

If A=[{:(8,0),(4,-2),(3,6):}]andB=[{:(2,-2),(4,2),(-5,1):}] , then find the matrix X , such that 2A+3X=5B.

Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):} Then, g(x) in [0, 2] is

Let f(x) =|{:(secx,x^(2),x),(2sinx,x^(3),2x^(2)),(tan3x,x^(2),x):}|lim_(x to 0)f(x)/(x^(4)) is equal to

If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),( 2 cos pix + tan ^(-1)x ,,, 1 lt x le 2):} is differentiable in [0,2] then: ([.] denotes greatest integer function)

If b gt 1, x gt 0 and (2x)^(log_(b) 2)-(3x)^(log_(b) 3)=0 , then x is