RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Injection test: Let x and y be any two elements in the domain (R), such that f(x) = f(y).

f(x) = f(y)

5x³ + 4 = 5y³ + 4

5x³ = 5y³

x³ = y³

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

5x³ + 4 = y

5x³ = y - 4

$\text{x}^3=\frac{\text{y}-4}{5}$

$\text{x}=\sqrt[3]{\frac{\text{y}-4}{5}}\in\text{R}$

So, f is a surjection and f is a bijection.