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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^4+2), why is it not onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^4+2) है, तो यह आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because a value like (1) is not obtainedक्योंकि (1) जैसा मान नहीं मिलता
Step 1: (x^4\ge0), so (x^4+2\ge2). Step 2: The codomain (\mathbb{R}) contains (1), which is not in the range. Step 3: Check the minimum value of even-power functions while testing onto nature.चरण 1: (x^4\ge0), इसलिए (x^4+2\ge2)। चरण 2: सहप्रांत (\mathbb{R}) में (1) है, जो परास में नहीं आता। चरण 3: सम घात वाले फलन का न्यूनतम मान देखकर आच्छादीपन जांचें।
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