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Question
Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = 3 − 4x
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Solution
f : R → R, defined by f(x) = 3 − 4x
Injection test:
Let x and y be any two elements in the domain (R), such that f(x) = f(y).
f(x) = f(y)
3−4x = 3−4y
−4x = −4y
x = y
So, f is an injection .
Surjection test:
Let y be any element in the co-domain (R), such that f(x) = y for some element x in R (domain).
f(x) = y
3 − 4x = y
4x = 3−y
`x = (3-y)/4`∈ R
So, f is a surjection and f is a bijection.
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