Question

What is the inverse of f(x) = 1 - 3 in the group of all bijections from ℝ onto ℝ?

Answer 1

There is no inverse for the constant function f(x) = 1 - 3 in the group of bijections from ℝ onto ℝ because a constant function is not bijective.

Step-by-step explanation:

To find the inverse function of f(x) = 1 - 3, which is a constant function, we need to consider if such an inverse exists. In the context of bijections or bijective functions, an inverse exists only when every x in the domain has a unique y in the codomain, and vice versa. A constant function does not satisfy this since it maps every x to the same value, hence it is not a bijection, and no inverse exists for this function within the group of all bijections from ℝ onto ℝ.