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in Sets, relations and functions by (53.3k points)
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For x > 0, let f (x) = x2/3 (6 - x)1/3 and g(x) = x.In x which of the following is/are true?

(A)  Exactly 1 real solution exist for the equation f (x) = g (x) 

(B)  f (x) ≥ g(x),∀x ∈ [1,4]

(C)  For y = f(x) , (6 ,0) is a point of the inflexion

(D) For x ∈(0, 4) the equation f (x) = f-1(x) has only one real solution

1 Answer

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by (53.1k points)
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Best answer

Correct option (A, C, D)

f (x) is a concave downward function for 0 < x < 6, while g (x) is a concave upward function for x > 0. Moreover, g f (3) > f(3)

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