यदि \(g\circ f\) एकैकी है, तो निश्चित रूप से कौन-सा निष्कर्ष सही है?
If \(g\circ f\) is one-one, which conclusion is definitely correct?
Explanation opens after your attempt
Correct Answer
A. \(f\) एकैकी है/(f) is one-one
Step 1
Concept
Suppose (f(a)=f(b)).
Step 2
Why this answer is correct
Then (g(f(a))=g(f(b))), so (\(g\circ f\)(a)=\(g\circ f\)(b)). Since \(g\circ f\) is one-one, (a=b).
Step 3
Exam Tip
In composition questions, apply the definition directly. चरण 1: मान लें (f(a)=f(b))। चरण 2: तब (g(f(a))=g(f(b))), यानी (\(g\circ f\)(a)=\(g\circ f\)(b))। \(g\circ f\) एकैकी है, इसलिए (a=b)। चरण 3: संयोजन वाले प्रश्नों में परिभाषा को सीधे लागू करें।
Mathematics Answer, Explanation and Revision Hints
यदि \(g\circ f\) एकैकी है, तो निश्चित रूप से कौन-सा निष्कर्ष सही है? / If \(g\circ f\) is one-one, which conclusion is definitely correct?
Correct Answer: A. \(f\) एकैकी है / (f) is one-one. Explanation: चरण 1: मान लें (f(a)=f(b))। चरण 2: तब (g(f(a))=g(f(b))), यानी (\(g\circ f\)(a)=\(g\circ f\)(b))। \(g\circ f\) एकैकी है, इसलिए (a=b)। चरण 3: संयोजन वाले प्रश्नों में परिभाषा को सीधे लागू करें। / Step 1: Suppose (f(a)=f(b)). Step 2: Then (g(f(a))=g(f(b))), so (\(g\circ f\)(a)=\(g\circ f\)(b)). Since \(g\circ f\) is one-one, (a=b). Step 3: In composition questions, apply the definition directly.
Which concept should I revise for this Mathematics MCQ?
Suppose (f(a)=f(b)).
What exam hint can help solve this Mathematics question?
In composition questions, apply the definition directly. चरण 1: मान लें (f(a)=f(b))। चरण 2: तब (g(f(a))=g(f(b))), यानी (\(g\circ f\)(a)=\(g\circ f\)(b))। \(g\circ f\) एकैकी है, इसलिए (a=b)। चरण 3: संयोजन वाले प्रश्नों में परिभाषा को सीधे लागू करें।
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