Functions Question 450
Question: Which of the following statements is incorrect
Options:
A) x sgn x = $ | x | $
B) $ | x | $ sgn x = x
C) $ x(sgn,x)(sgn,x)=x $
D) $ | x |,{{(sgn,x)}^{3}}=| x | $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Checking the options a. LHS $ =x\sgn x=x\times (+1)=xifx>0 $ $ x\times 0=0ifx=0 $ $ x\times (-1)=-xifx<0 $ $ =| x |=RHS $ b. LHS $ =| x |sgnx=(+x)\times (+1)=xifx>0 $ $ 0\times 0=0if,x=0 $ $ (-x)\times (-1)=xifx<0 $ Therefore, statement is correct. c. $ LHS=(x(sgnx))\times sgn,x=| x |\sgn x $ (from (a))=x (from (b))= RHS d. LHS $ (| x |sgn,x){{(sgn,x)}^{2}}=x{{(sgn,x)}^{2}}(from(b)) $ $ =| x |\times (sgnx), $ (From (a)) $ =x $ (From (b)) $ \ne RHS $ Therefore, statement is incorrect.
BETA
