Question:
Range of $f(x) = sin^{-1} x + tan^{-1} x + sec^{-1} x$ is
Range of $f(x) = sin^{-1} x + tan^{-1} x + sec^{-1} x$ is
Updated On: Jul 6, 2022
- $\left(\frac{\pi}{4}, \frac{3\pi }{4}\right)$
- $\left[\frac{\pi}{4}, \frac{3\pi }{4}\right]$
- $\left\{\frac{\pi}{4}, \frac{3\pi }{4}\right\}$
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
$f(x ) = sin^{-1}x + tan^{-1}x + sec^{-1}x$
Domain of $sin^{-1}x = [-1,1]$
Domain of $tan^{-1}x = ( -\infty, \infty)$
Domain of $sec^{-1} = ( -\infty, \infty) - (-1,1)$
Domain of $f(x) = [ - 1, 1] \cap (-\infty, \infty) \cap [(-\infty, \infty) - (-1, 1)]$
$ = \{-1,1\}$
Now $f(-1 ) = sin^{-1} + tan^{-1}( - 1 ) + sec^{-1}( -1 )$
$= -\frac{\pi}{2} - \frac{\pi }{4} +\pi = \frac{\pi }{4}$
and $f\left(1\right) = sin^{-1}\left(1\right) + tan^{-1}\left(1\right) + sec^{-1}\left(1\right)$
$= \frac{\pi }{2} + \frac{\pi }{4} + 0$
$= \frac{3\pi }{4}$
Range of $f\left(x\right) = \left\{\frac{\pi }{4}, \frac{3\pi }{4}\right\}$
Was this answer helpful?
0
0
Top Questions on range
- At an election, a voter may vote for any number of candidates not exceeding the number to be elected. If 4 candidates are to be elected out of the 12 contested in the election and voter votes for at least one candidate, then the number of ways of selections is:
- If \( 22 P_{r+1} : 20 P_{r+2} = 11 : 52 \), then \( r \) is equal to:
- A person invites a party of 10 friends at dinner and places so that 4 are on one round table and 6 on the other round table. Total number of ways in which he can arrange the guests is:
- How many different nine-digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?
- The number of arrangements of all digits of 12345 such that at least 3 digits will not come in its position is:
View More Questions
Concepts Used:
Range
The range in statistics for a provided data set is the difference between the highest and lowest values. For instance, if the provided data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.
Thus, the range could also be described as the difference between the highest observation and lowest observation. The acquired result is called the range of observation. The range in statistics states the spread of observations.
