Paragraph: Let f be a differentiable function satisfying [3] f(x+y) = [3] f(x) + [3] f(y) +1 x, y R and f^ (0)=3 Question: If x₀ is solution of the equation f(x)=f⁻¹(x) , then ⁻¹ ( 2 x₀ )+4 ⁻¹ ( x₀ 2 ) is equal to:

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Correct answer: C. 2

aligned & f(x)=(x-1)^3 & f(x)-x^3=-3 x^2+3 x-1=h(x) aligned (i) Clearly, y=h(|x|) is non-derivable at exactly one point. (ii) f(x) and f⁻¹(x) meet on the line y=x at x=x₀ where 2 ⁻¹ ( 2 x₀ )+4 ⁻¹ ( x₀ 2 )= (2 -2 x₀ )+4 x₀ 2 =2

Paragraph: Let f be a differentiable function satisfying [3] f(x+y) = [3] f(x) + [3] f(y) +1 x, y R and f^ (0)=3 Question: If x₀ is solution of the equation f(x)=f⁻¹(x) , then ⁻¹ ( 2 x₀ )+4 ⁻¹ ( x₀ 2 ) is equal to:

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