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If f(x) = x + 1 and g(x) = 1/x, what is the domain of (f + g)(x)?यदि f(x) = x + 1 और g(x) = 1/x हों, तो (f + g)(x) का डोमेन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ℝ \ {0}ℝ \ {0}
The sum is (f + g)(x) = x + 1 + 1/x. Since 1/x is undefined at x = 0, while x + 1 is defined for every real number, the sum is defined for all real numbers except 0. Thus its domain is ℝ \ {0}.योग फलन (f + g)(x) = x + 1 + 1/x है। 1/x, x = 0 पर अपरिभाषित है, जबकि x + 1 हर वास्तविक संख्या के लिए परिभाषित है। इसलिए योग फलन का डोमेन शून्य को छोड़कर सभी वास्तविक संख्याएँ, अर्थात् ℝ \ {0}, है।
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