Range of the function f(x) = x^2 + x + 2 x^2 + x + 1 ; ;x R is - Vidyadip

MCQ

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

A
$(1,\;\infty )$
B
$(1,\;11/7]$
✓
$(1,\;7/3]$
D
$(1,\;7/5]$

✓

Answer

Correct option: C.

$(1,\;7/3]$

c
(c) $f(x) = 1 + \frac{1}{{{{\left( {x + \frac{1}{2}} \right)}^2} + \frac{3}{4}}}$

==> Range $ = (1,\,7/3]$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11- 2. Relation and Function→STD 11- 2. Relation and Function — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Middle point of the chord of the circle ${x^2} + {y^2} = 25$ intercepted on the line $x - 2y = 2$ is

Let $a_1, a_2, a_3, \ldots, a_{11}$ be real numbers satisfying $a_1=15,27-2 a_2>0$ and $a_k=2 a_{k-1}-a_{k-2}$ for $k=3,4, \ldots$,

$11$. If $\frac{a_1^2+a_2^2+\ldots+a_{11}^2}{11}=90$, then the value of $\frac{a_1+a_2+\ldots+a_{11}}{11}$ is equal to

If $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ then :

If $A, B, C$ are angles of a triangle, then $\sin 2A + \sin 2B - \sin 2C$ is equal to

If a vertex of a triangle is $(1, 1)$ and the mid points of two sides through this vertex are $(-1, 2)$ and $(3, 2)$, then the centroid of the triangle is

Choose the correct answer. If $z$ is a complex number, then:

The line $x\cos \alpha + y\sin \alpha = p$ will touch the parabola ${y^2} = 4a(x + a)$, if

Evaluate: $\lim_{\text{n} \rightarrow \infty} \dfrac{\text{n}!}{(\text{n}+1)!-\text{n}!}$

Let $\alpha, \beta$ be two roots of the equation $x^{2}+(20)^{\frac{1}{4}} x+(5)^{\frac{1}{2}}=0$. Then $\alpha^{8}+\beta^{8}$ is equal to:

Out of $10$ points in a plane $6$ are in a straight line. The number of triangles formed by joining these points are