Let f(x) = |x – 1|. Then, A. f(x2) = [f(x)]2 B. f(x + y) = f(x) f( – InterviewSolution

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Let f(x) = |x – 1|. Then, A. f(x2) = [f(x)]2 B. f(x + y) = f(x) f(y) C. f(|x|) = |f(x)| D. None of these

Answer»

Option : (D)

f(x) = |x-1|

f(x²) = |x²-1|

f(x)²= (x-1)²

= x²+1-2x

So,

f(x²) ≠ [f(x)]²

f(x + y) = |x+y-1|

f(x)f(y) = (x-1)(y-1)

So,

f(x + y) ≠ f(x)f(y)

f(|x|) = ||x|-1|

Therefore,

Option D is correct.

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