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If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x^2+2x+5}{x^2+2x+2}), what is the range of (f)?यदि (f:\mathbb{R}\to\mathbb{R}) को (f(x)=\frac{x^2+2x+5}{x^2+2x+2}) से दिया गया है, तो (f) का परिसर क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\left(1,\frac{5}{2}\right])(\left(1,\frac{5}{2}\right])
Here (x^2+2x+2=(x+1)^2+1) and (f(x)=1+\frac{3}{(x+1)^2+1}). The maximum is (\frac{5}{2}), and (1) is never attained.(x^2+2x+2=(x+1)^2+1) और (f(x)=1+\frac{3}{(x+1)^2+1}) है। अधिकतम (\frac{5}{2}) मिलता है और (1) कभी नहीं मिलता।
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