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If (f:[2,\infty)\to[0,\infty)) and (f(x)=\sqrt{x-2}), what is (f^{-1}(x))?यदि (f:[2,\infty)\to[0,\infty)) तथा (f(x)=\sqrt{x-2}) हो तो (f^{-1}(x)) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (x^2+2)(x^2+2)
Step 1: Write (y=\sqrt{x-2}). Step 2: Squaring both sides gives (y^2=x-2), so (x=y^2+2). Step 3: When writing the inverse, the domain and range are interchanged.चरण 1: (y=\sqrt{x-2}) लिखें। चरण 2: दोनों ओर वर्ग करने पर (y^2=x-2) इसलिए (x=y^2+2)। चरण 3: व्युत्क्रम लिखते समय नए प्रांत और परास भी बदल जाते हैं।
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