FunctionHard
Question
In the following functions defined from [-1, 1] to [-1, 1] , then functions which are not bijective are
Options
A.sin (sin-1x)
B.2/π sin-1(sin x)
C.(sgn x) ln ex
D.x3 sgn x
Solution
f : [-1, 1] → [-1, 1]
(A) f(x) = sin (sin-1 x) = x, x ∈ [-1, 1]
Bijective function y ∈ [-1, 1]
(B) f(x) =
sin-1 (sin x) = 
, x ∈ [-1, 1]
Not bijective y ∈
(C) f(x) (sgn x) (ln ex) =
Not bijective
(D) f(x) = x3 sgn x =
Not bijective
(A) f(x) = sin (sin-1 x) = x, x ∈ [-1, 1]
Bijective function y ∈ [-1, 1]
(B) f(x) =
sin-1 (sin x) = , x ∈ [-1, 1]Not bijective y ∈
(C) f(x) (sgn x) (ln ex) =
Not bijective
(D) f(x) = x3 sgn x =
Not bijective
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