AP EAMCET · Maths · Functions
If and are two functions such that is a bijection, then which one of the following is always true?
- A and are bijections
- B is an injection and is a surjection
- C is a surjection and is an injection
- D is a bijection but is not a bijection
Answer & Solution
Correct Answer
(B) is an injection and is a surjection
Step-by-step Solution
Detailed explanation
Given: f:A→B and g:B→C And, gof:A→C is a bijection. Let x, y∈A such that fx=fy. Then, fx=fy ⇒gfx=gfy ⇒gofx=gofy ⇒x=y; ∵gof:A→C is one-one Hence, fx is an injection. Now, Let z be an arbitrary…
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