Greatest value of the function, f(x) = - 1 + 2 2^x ^2 + 1 is - Vidyadip

MCQ

Greatest value of the function, $f(x) = - 1 + \frac{2}{{{2^x}^2 + 1}}$ is

A
$1$
B
$3/2$
C
$2/3$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
$f(x)=-1+\frac{2}{2^{x^{2}}+1}$

Clearly $f(x)$ in an even function and $f(x)$ is greatest

when $\frac{2}{2^{x^{2}}+1}$ is greatest.

(given)

Also, $\frac{2}{2^{x^{2}}+1}$ is greatest when $2^{x^{2}}+1$ is least,

which occurs when $x=0.$

Hence greatest value is $f(0)=0.$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The point of intersection of the lines $\frac{{x + 1}}{3} = \frac{{y + 3}}{5} = \frac{{z + 5}}{7}$ and $\frac{{x - 2}}{1} = \frac{{y - 4}}{3} = \frac{{z - 6}}{5}$is

A particle starts at the origin and moves along the $x$-axis in such a way that its velocity at the point $(x, 0)$ is given by the formula $\frac{{dx}}{{dt}} = {\cos ^2}\pi x.$ Then the particle never reaches the point on

The range of the function,

$\mathrm{f}(\mathrm{x})=\log _{\sqrt{5}}(3+\cos \left(\frac{3 \pi}{4}+\mathrm{x}\right)+\cos \left(\frac{\pi}{4}+\mathrm{x}\right)+\cos \left(\frac{\pi}{4}-\mathrm{x}\right)$

$-\cos \left(\frac{3 \pi}{4}-\mathrm{x}\right))$ is :

A determinant is chosen at random. The set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that value of the determinant chosen is positive, is

Let $y = f(x)$ be a thrice differentiable function in $(–5, 5).$ Let the tangents to the curve $y=f(x)$ at $(1, f(1))$ and $(3, f(3))$ make angles $\frac{\pi}{6}$ and $\frac{\pi}{4}$, respectively with positive $x-$axis. If $27 \int_1^3\left(\left(f^{\prime}(t)\right)^2+1\right) f^{\prime \prime}(t) d t=\alpha+\beta \sqrt{3}$ where $\alpha, \beta$ are integers, then the value of $\alpha + \beta$ equals

If ${a_1},{a_2},....{a_n}$ are positive real numbers whose product is a fixed number $c$, then the minimum value of ${a_1} + {a_2} + ...$ $ + {a_{n - 1}} + 2{a_n}$ is

Let two straight lines drawn from the origin $O$ intersect the line $3 x+4 y=12$ at the points $P$ and $\mathrm{Q}$ such that $\triangle \mathrm{OPQ}$ is an isosceles triangle and $\angle \mathrm{POQ}=90^{\circ}$. If $l=\mathrm{OP}^2+\mathrm{PQ}^2+\mathrm{QO}^2$, then the greatest integer less than or equal to $l$ is :

The graph of the conic $x^2-(y-1)^2=1$ has one tangent line with positive slope that passes through the origin. The point of the tangency being $(a, b)$ then find the value of $\sin ^{-1}\left(\frac{a}{b}\right)$

The area between the parabola $y = {x^2}$ and the line $y = x$ is

The coefficient of ${x^{32}}$ in the expansion of ${\left( {{x^4} - \frac{1}{{{x^3}}}} \right)^{15}}$ is