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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^4-x^2), (f) is not onto because which value cannot be obtained?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^4-x^2), तो (f) आच्छादक नहीं है क्योंकि कौन-सा मान नहीं मिल सकता?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (-1)(-1)
Step 1: Put (t=x^2\ge0), so (x^4-x^2=t^2-t). Step 2: The minimum value of (t^2-t) is (-\frac{1}{4}), so (-1) cannot be obtained. Step 3: For fourth-degree expressions in (x^2), substituting (t=x^2) helps find the range.चरण 1: (x^4-x^2=(x^2)^2-x^2) रखकर (t=x^2\ge0) लें। चरण 2: (t^2-t) का न्यूनतम मान (-\frac{1}{4}) है, इसलिए (-1) नहीं मिल सकता। चरण 3: चौथी घात वाले फलनों में (t=x^2) रखकर परास समझना आसान होता है।
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