The range of the function, f(x)=(1+ ^ -1 x)(1+ ^ -1 x) is: 1. (- … - Vidyadip

Question

The range of the function, $\text{f(x)}=(1+\sec^{-1}\text{x})(1+\cos^{-1}\text{x})$ is:

$(-\infty,\infty)$
$(-\infty,0]\cup[4.\infty)$
$\big\{0,(1+\pi^2)\big\}$
$[1.(1+\pi)^2]$

✓

Answer

$[1.(1+\pi)^2]$

Solution:
$\text{f(x)}=(1+\sec^{-1}(\text{x}))(1+\cos^{-1}(\text{x}))$

Here the limiting component is $\cos−1(\text{x}),$ since the domain of $\cos−1(\text{x}),$ is [−1, 1].
Therefore,
$\text{f}(1)=(1+0)(1+0)$
$=1$
$\text{f}(−1)=(1+\pi(1+\pi)$
$=(1+\pi)^2 $
Hence range of $\text{f(x)}=[1,(1+\pi)^2]$

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 INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Choose the correct answer from the given four option.
Solution of the differential equation $\tan\text{y}\sec^2\text{xdx} + \tan\text{x }\sec^2\text{ydy}=0$is:

$\tan\text{x}+\tan\text{y}=\text{k}$
$\tan\text{x}-\tan\text{y}=\text{k}$
$\frac{\tan\text{x}}{\tan\text{y}}=\text{k}$
$\tan\text{x}.\tan\text{y}=\text{k}$

Function $\text{f}(\text{x})=\cos\text{x}-2\lambda\text{x}$ is monotonic decreasing when:

$\lambda>\frac{1}{2}$
$\lambda<\frac{1}{2}$
$\lambda<2$
$\lambda>2$

Five persone entered the lift cabin on the ground floor of an $8$ floor house. Suppose that each of them independently and with equal probability can leave the cabin at any flor beginning with the first, then the probability of all $5$ persons leaving at different floors is,

If $\text{y}=\tan^{-1}\Big\{\frac{\log(\frac{\text{e}}{\text{x}})^2}{\log(\frac{\text{e}}{\text{x}})^2}\Big\}+\tan^{-1}\Big(\frac{3-2\log,\text{x}}{1-6\log,\text{x}}\Big)$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}=$

2
1
0
-1

If $A = [a_{ij}]$ is a scalar matrix of order $n \times n$ such that $a_{ij} = k,$ for all $i,$ then trace of $A$ is equal to$:$

Consider a LPP given by
Minimum Z = 6x + 10y
Subjected to x ≥ 6, y ≥ 2, 2x + y ≥ 10, x ≥ 0, y ≥ 0
Redundant constraints in this LPP are

The d.rs of the lines x = ay + b, z = cy + d are:

Let $E$ be an event of a sample space $S$ of an experiment then $P(S \mid E)=$

If $A$ is a matrix of order $m \times n$ and $B$ is a matrix such that $AB^{T }$ and $B^{T }A$ are both defined, then the order of matrix $B$ is:

A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 22 green balls and one blue ball is

$\frac{167}{168}$
$\frac{1}{28}$
$\frac{2}{21}$
$\frac{3}{28}$