MorallyObtuse said:Homework Statement
For each of the following bijective functions find the range S and the inverse:
a.) f : x |→ x² - 1 (x ∈ R, x ≥ 0)
b.) f : x |→ (x + 1)² ((x ∈ R, x ≤ -2)...Not sure how to do this one, help please
A bijective function is a type of mathematical function that has a one-to-one correspondence between its input and output. This means that for every input, there is a unique output and vice versa.
A function can be determined as bijective if it is both injective (one-to-one) and surjective (onto). This means that every element in the output has a corresponding element in the input, and each input has a unique output.
The range of a bijective function is the set of all possible output values of the function. This means that every output value can be achieved by at least one input value.
The inverse of a bijective function is calculated by switching the input and output variables of the original function. This means that the input of the original function becomes the output of the inverse function, and vice versa.
The inverse of a bijective function is important because it allows us to solve for the original input value given an output value. This can be useful in many real-world applications, such as finding the original price of a discounted item or determining the initial value of an investment based on its final value.