Let f(x)=x^2-2 a x+a-2 and g(x)= [2+ ⁻¹ ( 2 x 1+x^2 ) ] . If the set of real values of ' a ' for which .f g(x) ] 0 x R is (k₁, k₂ ) , then the equation h(x)= [5 k₁-3 k₂ . has 6 distinct solution where f(x)=|x-2| and h(x)=f f(f( . .(f(x))) .

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Let f(x)=x^2-2 a x+a-2 and g(x)= [2+ ⁻¹ ( 2 x 1+x^2 ) ] . If the set of real values of ' a ' for which .f g(x) ] 0 x R is (k₁, k₂ ) , then the equation h(x)= [5 k₁-3 k₂ . has 6 distinct solution where f(x)=|x-2| and h(x)=f f(f( . .(f(x))) . .) _ n limes , then find the value of ' n ' (where [ . ] denotes the greatest integer function)

Quantrex Academy · Accepted Answer

Correct answer: 3

g(x)=2+ [ ⁻¹ ( 2 x x^2+1 ) ]=2+-2 or -1 or 0 or 1 So. range of g(x)= 0,1,2,3 for f(g(x)) 0 x R f (0) 0 and f (3) 0 a 2 and a 7 5 a ( 7 5 , 2 ) So, k₁= 7 5 , k₂=2 thus [5 k₁-2 k₂ ]=1 Where f(x)=|x-2| . clearly n=3f(x)=x^2-2 a x-a-2

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