If y = f(x) and f(x) = (1–x)(1+x), which of the following is true?
Explanation:
y = f(x) = 1-x1+x
⇒ y(1 + x) = 1 – x
⇒ y + xy = 1 – x
⇒ x + xy = 1 – y
⇒ x(1 + y) = (1 – y)
⇒ x = 1-y1+y = f(y)
Since here, y = f(x) and x = f(y), the given function refleccts on itself.
Hence, option (d).
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