Injective Functions

1-1 function. Function f maps distinct elements of its domain to distinct elements.

Simply put, all x values will have unique y values. 2 different x values, CANNOT have the same y value.

Formal Definition

$\forall x_1,x_2\in A:(f(x_1)=f(x_2))⟹(x_1=x_2)$

Kernel Definition

$T$ is injective $⟺$ $ker(T)=\{0\}$

List of injective functions

• Exponential functions
• Logarithms
• Odd Function

Theorems

• Kernels and Injectivity Theorem