Which one of the following is f(x)?
Direction: Consider the following for the two (02) items that follow : Let f \circ g(x)=\cos^{2}\sqrt{x} and g \circ f(x)=|\cos x|.
- A. \cos x
- B. \cos x^{2}
- C. \cos^{2}x ✓
- D. \cos|x|
Correct Answer: C. \cos^{2}x
Explanation
We are given f(g(x)) = \cos^2\sqrt{x} and g(f(x)) = |\cos x|. If we assume g(x) = \sqrt{x} and f(x) = \cos^2 x, then g(f(x)) = \sqrt{\cos^2 x} = |\cos x| and f(g(x)) = \cos^2(\sqrt{x}). This satisfies both conditions perfectly. Thus, f(x) = \cos^2 x.
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