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Question

If f(x)=|x1|, then which of the following are true?

A
f(x2)=(f(x))2
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B
f(x+y)=f(x)+f(y)
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C
f(|x|)=|f(x)|
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D
None of the above
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Solution

The correct option is D None of the above
Given that f(x)=|x1|.
f(x2)=|x21|=|x1||x+1|
But, (f(x))2=|x1|2=|x1||x1|f(x2).

Now, f(x+y)=|x+y1|.
Whereas, f(x)+f(y)=|x1|+|y1|f(x+y).

Also, f(|x|)=||x|1|.
But, |f(x)|=|x1|f(|x|).

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