Can anyone please help me in equation form with the answers to the following questions?

1. Give the range of the functiony= tan^-1x

2. Give the value of tan^-1 5

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- Jun 11th 2006, 06:44 PMKiwigirlSolve equations
Can anyone please help me in equation form with the answers to the following questions?

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

2. Give the value of tan^-1 5 - Jun 11th 2006, 06:56 PMThePerfectHackerQuote:

Originally Posted by**Kiwigirl**

$\displaystyle y\in (-\pi/2,\pi/2)$

The second way. The function $\displaystyle \tan^{-1}(x)$ is defined as the inverse function of the function,

$\displaystyle \tan x \mbox{ on } -\pi/2<x<\pi/2$. 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 $\displaystyle (-\pi/2,\pi/2)$ thus the range of $\displaystyle \tan^{-1}(x)$ is $\displaystyle (-\pi/2,\pi/2)$

There is actually a third way (much more advanced). Find all such $\displaystyle y$ such as the equation $\displaystyle y=\tan^{-1}(x)$ has a solution.