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entries of column](C) Range ott is a singluun(D) sgn (f(x)) = 1 where son x denotes signuumn Il contains their range. Match the entrieColumn-IIColumn I contains functions and columnentries of column II.0.9Column-1(P)(0, 1)OS(a) f(x) = sin ( 1+1x1)(B) 8(x) = cos - ( 11 )(C) h(x)= tan-(19x)D) kw=cot (11x1)

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to bus UUTULUS SiguUITI TUNIULUI UIA.column I with the QColumn I contains functions and column Il contains their range. Match the entries of column I wirentries of column II.Column-IColumn-II(P)(0, 1)(A) f(x)=sin ( 1 )®) g(x) = cos (+18EC) h(x)= tan (1981kx) = cot (1218)c) (474

0.8Let f(x)= In x and g(x)=x2-1Column-I contains composite functions and column-II contains their domain. Match the entries of column-I with their corresponding answer is column-II.Column-1Column-II(P) (1,00)(A) fog(B) gof(0) (0,00)(700, -1) U (1,00)|(D) gog(0,0)fof

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If f(x)=ln(1+x)-(tan^(-1)x)/(1+x) , (for x> 0) then sgn f(x) is ( sgn represents signum function)

Domain (D) and range (R) of f(x)=sin^(-1)(cos^(-1)[x]), where [.] denotes the greatest integer function, is

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Verify the Lagrange's theorem for the following functions: (a) f(x) = x^(3) in [-1,1] (b) f(x) = sin x in [0,pi/2] ( c) f(x) = x^(n) in [-1,1], n in Z^(+) ( d) f(x) =2x^(2) - 7x + 10, x in [2,5]