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Question: Range of the function \(f(x) = \frac{x^{2} + x + 2}{x^{2} + x + 1};x \in R\)is...

Range of the function f(x)=x2+x+2x2+x+1;x∈Rf(x) = \frac{x^{2} + x + 2}{x^{2} + x + 1};x \in Ris

A

(1,∞)(1,\infty)

B

(1,11/7)(1,11/7)

C

(1,7/3](1,7/3\rbrack

D

(1,7/5](1,7/5\rbrack

Answer

(1,7/3](1,7/3\rbrack

Explanation

Solution

f(x)=1+1(x+12)2+34f(x) = 1 + \frac{1}{\left( x + \frac{1}{2} \right)^{2} + \frac{3}{4}} ⇒ Range =(1,7/3]= (1,7/3\rbrack.