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If (f(x)=\frac{1}{x-2}) and (g(x)=\sqrt{x+3}), what is the domain of ((fg)(x))?यदि (f(x)=\frac{1}{x-2}) और (g(x)=\sqrt{x+3}) हों, तो ((fg)(x)) का प्रांत क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ( [-3,\infty)\setminus{2} )( [-3,\infty)\setminus{2} )
The root needs (x\ge -3) and the denominator needs (x\ne 2). For a product, take the common domain of both functions.मूल के लिए (x\ge -3) और हर के लिए (x\ne 2) चाहिए। गुणन में भी दोनों फलनों का सामान्य प्रांत लिया जाता है।
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