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AP EAMCET202120 Aug 2021Evening ShiftMathematicsFunctionsActual

If f : R → R and g : R → R are two functions defined by f x = a x + b a ≠ 0 ∀ x ∈ R and g x = c x 3 + d c ≠ 0 ∀ x ∈ R , then f o g - 1 x =

Options

  1. Ax - a d + b a c 1 2
  2. Bx + a d - b a c 1 3
  3. Cx - a d - b a c 1 3
  4. Dx + a d + b a c 1 3

Correct answer

C. x - a d - b a c 1 3

Step-by-step solution

Given, f x = a x + b and g x = c x 3 + d f o g x = f g x f o g x = a g x + b = a c x 3 + d + b Let, y = a c x 3 + a d + b x 3 = y - a d - b a c x = y - a d - b a c 1 3 Hence, f o g - 1 x = x - a d - b a c 1 3

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