AP EAMCET · Maths · Functions
If \(f: A \rightarrow B\) and \(g: B \rightarrow C\) are two functions such that \(g \circ f: A \rightarrow C\) is a bijection, then which one of the following is always true?
- A f and g are bijections
- B f is an injection and g is a surjection
- C f is a surjection and g is an injection
- D f is a bijection but g is not a bijection
Answer & Solution
Correct Answer
(B) f is an injection and g is a surjection
Step-by-step Solution
Detailed explanation
If \(f: A \rightarrow B\) and \(g: B \rightarrow C\) are two function such that \(g \circ f: A \rightarrow C\) is bijection. As, \(g \circ f\) is one-one for \(x, y\) Let \(f(x)=f(y)\) \(g \circ(f(x))=g \circ(f(y))\) \[ \Rightarrow \quad g f(x)=g f(y) \Rightarrow x=y \]…
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