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Question
Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : g(x) = |x|
Solution
g(x) = |x|
Injection test:
Let x and y be any two elements in the domain (A), such that f(x) = f(y).
f(x) = f(y)
|x| = |y|
x = ± y
So, f is not one-one.
Surjection test :
For y = -1, there is no value of x in A.
So, f is not onto.
So, f is not bijective.
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