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f(x)= (20-x^4 )^ 1 / 4 for 0 < x < 5 , then f (f ( 1 2 ) ) is equal to

Options

  1. A2⁻⁴
  2. B2⁻³
  3. C2⁻²
  4. D2⁻¹

Correct answer

D. 2⁻¹

Step-by-step solution

We have, aligned f(x) & = (20-x^4 )^ 1 4 f ( 1 2 ) & = (20- 1 16 )^ 1 4 = ( 319 16 )^ 1 4 f [f ( 1 2 ) ] & =f [ ( 319 16 )^ 1 4 ] & = (20- 319 16 )^ 1 4 & = ( 1 16 )^ 1 4 = 1 2 =2⁻¹ aligned

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