# Find Domain

Printable View

• June 11th 2006, 06:44 PM
Kiwigirl
Solve equations

1. Give the range of the function y = tan^-1 x

2. Give the value of tan^-1 5
• June 11th 2006, 06:56 PM
ThePerfectHacker
1 Attachment(s)
Quote:

Originally Posted by Kiwigirl
$y\in (-\pi/2,\pi/2)$
The second way. The function $\tan^{-1}(x)$ is defined as the inverse function of the function,
$\tan x \mbox{ on } -\pi/2<x<\pi/2$. Now there is a rule that the range of the inverse function is the domain of the orignal function. Since the domain of the original function is $(-\pi/2,\pi/2)$ thus the range of $\tan^{-1}(x)$ is $(-\pi/2,\pi/2)$
There is actually a third way (much more advanced). Find all such $y$ such as the equation $y=\tan^{-1}(x)$ has a solution.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.914145827293396, "perplexity_flag": "middle"}