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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^6+1), which statement is correct?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^6+1) है, तो सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is not ontoयह आच्छादी नहीं है
Step 1: Since (x^6\ge0), (x^6+1\ge1). Step 2: The codomain (\mathbb{R}) contains (0) and negative values, which are not obtained. Step 3: Even powers with a positive shift have a range bounded below.चरण 1: (x^6\ge0), इसलिए (x^6+1\ge1)। चरण 2: सहप्रांत (\mathbb{R}) में (0) और ऋणात्मक मान हैं, जो प्राप्त नहीं होते। चरण 3: सम घात और धनात्मक जोड़ वाले फलन का परास नीचे से सीमित होता है।
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