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If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x|x|), what is (f^{-1}(4))?यदि (f:\mathbb{R}\to\mathbb{R}) को (f(x)=x|x|) से दिया गया है, तो (f^{-1}(4)) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2)(2)
Step 1: Since (4) is positive, the input (x) must be positive. Step 2: For positive (x), (f(x)=x^2), so (x^2=4). Step 3: The positive solution is (x=2).चरण 1: (4) धनात्मक है, इसलिए आगत (x) भी धनात्मक होगा। चरण 2: धनात्मक (x) पर (f(x)=x^2), इसलिए (x^2=4)। चरण 3: धनात्मक हल (x=2) है।
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