Classify the following functions as injection, surjection or bije… - Vidyadip

Question

Classify the following functions as injection, surjection or bijection:f : R → R, defined by f(x) = 3 - 4x

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Answer

f : R → R, defined by f(x) = 3 - 4xInjection 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
Therefore, 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
$\text{x}=\frac{3-\text{y}}{4}\in\text{R}$
Therefore, f is a surjection and f is a bijection.

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