Suppose f : A → B, g : B → C are both surjections. Prove thatg ◦ f : A → C is a surjection
Question
Solution 1
To prove that the composition of two surjective functions is also surjective, we need to show that for every element 'c' in the set C, there exists an element 'a' in the set A such that (g ◦ f)(a) = c.
Here are the steps:
- Since g : B → C is surjective, for every 'c' in C, there exists an elemen Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv
Similar Questions
Suppose f : A → B, g : B → C are both surjections. Prove thatg ◦ f : A → C is a surjection
Suppose f : A → B and g : B → C are both surjective functions.Prove that g ◦ f : A → C is surjective
If f A —> B and g : B —> C are injectivefunction, then gof: A —> C is an injectivefunction. Prove or disprove.
Suppose that f(5) = 1, f '(5) = 8, g(5) = −4, and g'(5) = 2. Find the following values.(a) (fg)'(5) (b) (f/g)'(5) (c) (g/f)'(5)
) Let f, g be differentiable functions on an interval I. Suppose that a, b ∈ Iwith f (b) ≥ g(b) and f ′(x) ≤ g′(x) on [a, b]. Show that f (x) ≥ g(x) on[a, b].