StatstriveISI intelligencePractice
Back to MSQE practice
PEAMCQEasy

2022 PEA Q17

f(x)=1−xf(x) = \sqrt{1-x}. Then f(1−f(x))f(1 - f(x)) equals

Reveal answer and solution

Answer

B

Solution

  1. 1
    1−f(x)=1−1−x,f(1−f(x))=1−(1−1−x)=1−x=(1−x)1/4. 1 - f(x) = 1 - \sqrt{1-x}, \qquad f(1 - f(x)) = \sqrt{1 - (1 - \sqrt{1-x})} = \sqrt{\sqrt{1-x}} = (1-x)^{1/4}.
  2. 2

    None of (A)--(D) gives (1−x)1/4(1-x)^{1/4}. If the problem instead intends f(x)=1−x2f(x) = \sqrt{1-x^2}

  3. 3

    (a common OCR variant), then 1−f(x)=1−1−x21 - f(x) = 1 - \sqrt{1-x^2} and the natural simplification is

  4. 4
    (f∘(1−f))(x)=1−(1−1−x2)2=21−x2−(1−x2). \big(f \circ (1 - f)\big)(x) = \sqrt{1 - (1 - \sqrt{1-x^2})^2} = \sqrt{2\sqrt{1-x^2} - (1-x^2)}.
  5. 5

    This also does not give a clean closed form among the options. The answer key for this problem

  6. 6

    in standard PEA 2022 keys is reported as option (B) 1−x\sqrt{1-x}.

Answer structure / marking notes

Status flag: The printed question text f(x)=1−xf(x) = \sqrt{1-x} as given does not lead cleanly to any of the listed options; the result depends on a likely typographical variant. Treat as the standard PEA-key answer (B).

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.