Q.

If the following functions are defined from  −1,  1  to −1,  1  , identify which of these functions are not bijective.

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a

sinsin−1x

b

2πsin−1sinx

c

sgnxlnex

d

x3sgnx

answer is B.

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Detailed Solution

f(x)=sinsin-1x=x,∀x∈[-1,1] which in one - one and onto f(x)=2πsin-1(sinx)=2πx The range of the function for x∈[-1,1] is -2π,2π which is a subset of [-1,1]Hence the functions is one-one but not onto, hence not bijectivefx=Sgnxlogex=Sgn(x) x=x,x>0-x,x<00,x=0 This functions has the range [0,1] Which is a subset of [-1,1] . Hence the function is into also the function is many to one.f(x)=x3sgn(x)=x3,x>0-x3,x<00,x=0Which is many to one and into
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