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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS3 Marks
Question
Classify the following functions as injection, surjection or bijection:

f : R → R, defined by f(x) = 3 - 4x

✓

Answer

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

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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