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प्रश्न
Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`
उत्तर
`f : A → A, given by f (x) = x/2 `
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/2 = y /2`
x = y
So, f is one-one.
Surjection test :
Let y be any element in the co-domain (A), such that f(x) = y for some element x in A(domain)
f(x) = y
`x/2 = y`
x = 2y, which may not be in A.
For example, if y = 1, then
x = 2, which is not in A.
So, f is not onto.
So, f is not bijective.
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