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Graph of a function y=f^ (x) is shown as If g(x)=|f(|x|)| , then find number of solution(s) of the equation g(g(x))= sgn (x^2-(k+1) x+ (k^2+1 ) ), k R . [Note: sgn (y) denotes the signum function of y_ . ]

Correct answer

16

Step-by-step solution

aligned & g(g(x))=1 , let g(x)=t & g(t)=1 t=0, t₁, t₂, t₃, t₄, t₅, t₆ & Where 1 < t₁ < 2,2 < t₂ < 3,3 < t₃ < 4, t₄, t₅, t₆ < 0 & . Now, array l g(x)=0 8 solutions g(x)=t₁ 8 solutions array 16 solutions & aligned

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