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If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=2x^3-1), what is (f^{-1}(x))?यदि (f:\mathbb{R}\to\mathbb{R}) को (f(x)=2x^3-1) से दिया गया है, तो (f^{-1}(x)) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\sqrt[3]{\frac{x+1}{2}})(\sqrt[3]{\frac{x+1}{2}})
Step 1: Put (y=2x^3-1). Step 2: Then (y+1=2x^3), so (x=\sqrt[3]{\frac{y+1}{2}}). Step 3: In inverse questions, isolate (x) first and then change the variable.चरण 1: (y=2x^3-1) मानें। चरण 2: (y+1=2x^3), इसलिए (x=\sqrt[3]{\frac{y+1}{2}})। चरण 3: प्रतिलोम में पहले (x) को अलग करें, फिर चर बदलें।
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