A function is said to be injective if each input (domain element) corresponds to a unique output (range element). This means that no two different input values can result in the same output value.
To check if a function is injective, we can use the horizontal line test. This involves drawing a horizontal line on the graph of the function and checking if the line intersects the graph at more than one point. If it does, then the function is not injective. Another method is to use algebra to show that no two different input values can result in the same output value.
The condition for a function to be injective is that for any two different input values, the corresponding output values must be different. In other words, the function cannot map different inputs to the same output.
Yes, a function can be both injective and surjective. A function that is both injective and surjective is called a bijective function. This means that each input has a unique output and every output has a corresponding input.
Injective functions have several important applications in mathematics, including in cryptography, computer science, and data analysis. They also play a crucial role in determining the inverse of a function, which is essential in solving many mathematical problems.
