यदि (f(x)=\frac{1}{x}) और (g(x)=x) हैं, तो ((f+g)(x)) का प्रांत और ((fg)(x)) का मान क्या है?
If (f(x)=\frac{1}{x}) and (g(x)=x), what are the domain of ((f+g)(x)) and the value of ((fg)(x))?
Explanation opens after your attempt
Correct Answer
A. \(\mathbb{R}\setminus{0}\), (1)
Concept
The domain of (f) is \(x\ne 0\), and \(fg=\frac{1}{x}\cdot x=1\). The product may simplify, but the domain comes from the original functions.
Why this answer is correct
The correct answer is A. \(\mathbb{R}\setminus{0}\), (1). The domain of (f) is \(x\ne 0\), and \(fg=\frac{1}{x}\cdot x=1\). The product may simplify, but the domain comes from the original functions.
Exam Tip
(f) का प्रांत \(x\ne 0\) है और \(fg=\frac{1}{x}\cdot x=1\)। उत्पाद सरल हो सकता है, पर प्रांत मूल फलन से तय होगा।
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