Assignment -1
Grade Class 12
Question:
<p>Range of sec<sup>-1</sup>x is</p>
<p style="display:inline">[0, <span class="math-tex">\(\pi\)</span>]</p>
<p style="display:inline"><span class="math-tex">\(\left[0, \frac{\pi}{2}\right]\)</span></p>
<p style="display:inline"><span class="math-tex">\(\left[0, \frac{\pi}{4}\right]\)</span></p>
<p style="display:inline"><span class="math-tex">\([0, \pi]-\left\{\frac{\pi}{2}\right\}\)</span></p>
Step-by-Step Solution
Key Concept: The range of sec⁻¹(x) is determined by restricting the domain of sec(x) to make it one-to-one. The standard convention restricts sec(x) to [0, π] excluding π/2 where secant is undefined, giving range [0, π] - {π/2}.
<p>To Find: The range of sec<sup>-1</sup>(x)<br />
Here, the inverse function is given by y = f<sup>-1</sup>(x)<br />
The graph of the function y = sec<sup>-1</sup>(x) can be obtained from the graph of<br />
Y = sec x by interchanging x and y axes.i.e, if (a, b) is a point on Y = sec x then (b, a) is the point on the function y = sec<sup>-1</sup>(x)<br />
Below is the Graph of the range of sec<sup>-1</sup>(x)<br />
<img src="https://media-mycbseguide.s3.amazonaws.com/images/imgur/2r0AbtG.jpg" style="height:150px; width:287px" /><br />
From the graph, it is clear that the range of sec<sup>-1</sup>(x) is restricted to interval<br />
<span class="math-tex">$[0, \pi]-\left\{\frac{\pi}{2}\right\}$</span></p>
Correct Answer: D