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