If the following functions are defined from [-1, 1] to [-1, 1], select those which are not bijective.
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a
sinsin-1x
b
1πsin-1sinx
c
sgnxlnex
d
x3sgnx
answer is B.
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Detailed Solution
fx=sinsin-1x=x∀x∈-1,1, which is one-one and onto.fx=2πsin-1sinx=2πxThe range of the function for x∈1-,1 is -2π,2π,which is a subset of [-1, 1].Hence, the function is one-one but not onto and, hence, is not bijective.fx=sgnxlnex=sinxx=x, x>0-x, x<00, x=0This function has range [0, 1] which is a subset of [-1, l].Hence, the function is into. Also, the function is many-one.fx=x3sgnx=x, x>0-x3, x<00, x=0which is many-one and into.