1.

Column 1: real valued function, Column-2: domain of the function, Column 3: range of the function. Match the following Column(s) (where [.] denotes the greatest integer function and {.} denotes fractional part function) Which of the following combination is correct?

Answer»

<P>(I)(iv)(P)
(I)(iv)`(R)`
(II)(ii)`(R)`
(III)(i)(S)

Solution :(I) `((3-1)^(3))/3le |x-1|^(3)+|x-3|^(3)ltoo`
(II) `u=sin(In((sqrt(4-x^(2)))/(1-x)))+cos(In((sqrt(4-x^(2)))/(1-x)))`
`:.0LE (sqrt(4-x^(2)))/(1-x) LT oo`
`-oo lt In ((sqrt(4-x^(2)))/(1-x))lt oo`
So, `-sqrt(2) le u le sqrt(2)`
(III) Let `|x+5|=t,g(t) in (0, 1/2]-{1/4}`
`g(t)=((t-2))/((t-2)(t+2))`
(IV) `thetalecos^(-1)xlepi`
`-oo lt In (cos^(-1)x)le In pi lt 2`


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