Question
Question: For A = [–1, 1] which of the following function(s) f : A → A are invertible:...
For A = [–1, 1] which of the following function(s) f : A → A are invertible:
A
f(x) = x/2
B
g(x) = sin (πx/2)
C
h(x) = |x|
D
k(x) = x2
Answer
g(x) = sin (πx/2)
Explanation
Solution
Clearly ‘C’ and ‘D’ are ruled out as these are many-one. Also f(x) = x/2 is one-one but not on-to. g(x) = sin(πx/2) is both one-one and onto