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If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^2+2x+2), what is the range of (f)?यदि (f:\mathbb{R}\to\mathbb{R}) और (f(x)=x^2+2x+2), तो (f) का परास क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ([1,\infty))([1,\infty))
Step 1: Complete the square: (x^2+2x+2=(x+1)^2+1). Step 2: Since ((x+1)^2\geq 0), the minimum value is (1). Step 3: Thus the range is ([1,\infty)).चरण 1: वर्ग पूर्ण करें: (x^2+2x+2=(x+1)^2+1)। चरण 2: ((x+1)^2\geq 0), इसलिए न्यूनतम मान (1) है। चरण 3: अतः परास ([1,\infty)) है।
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