If f:[0,3] [0,3] is defined by f(x)= array ll 1+x, & 0 x 2 3-x, & 2

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If f:[0,3] [0,3] is defined by f(x)= array ll 1+x, & 0 x 2 3-x, & 2 < x 3 array . , then fof is

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Correct answer: C. Discontinuous at x=1 and x=2

gathered g(x)=f(f(x))= cases f(1+x) ; & 0 x 2 f(3-x) & ; 2 Using Eqs, (i), (ii), (iii), we get g(x)= cases 2+x & ; 0 x < 1 2-x ; & 1 < x 2 4-x ; & 2 < x 3 cases Here, as g(x) change the inequality sign at x=1 and x=2 Thus, to check continuity at x=1 and x=2 Now, we will check the continuity of g(x) at aligned & x=1,2 At x=1, LHL & = _ x 1⁻ g(x)= _ x 1⁻ (2+x)=3 RHL & = _ x 1⁺ g(x)= _ x 1⁺ (2-x)=1 aligned As. LHL RHL g(x) is discontinuous at x=1 . aligned At x=2 LHL & = _ x 2⁻ g(x)= _ x 2⁻ (2-x)=0 RHL & = _ x 2⁺ g(x)

If f:[0,3] [0,3] is defined by f(x)= array ll 1+x, & 0 x 2 3-x, & 2 < x 3 array . , then fof is

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