Question

Write domain and range of y=tan'x.​

Answer 1

Concept:

Range is the possible output values shown on $y-$axis. Domain is the possbile input values that is shown in the $x-$axis.

Given:

$y=tan(x)$

Find:

Domain and range of the equation.

Solution:

According to the problem,

Setting the argument in $tan(x)$ equal to $\frac{\pi }{2}+\pi n$ so as to find where the expression is undefined.

$x=\frac{\pi }{2}+\pi n$, for any integer $n$

The domain is all set values of $x$ that makes the expression defined.

Set-Builder Notation,

$[x|x\neq \frac{\pi }{2}+\pi n]$, for any integer $n$

The range of tangents is all real numbers.

Interval Notation:

$(- \infty,\infty)$

Range will be,

$y$ belongs to $R$

Then, domain is: $[x|x\neq \frac{\pi }{2} +\pi n]$

Range is: $(- \infty,\infty),[y|y\in R]$

Graphing this will be,

Hence, the domain and range of $tan(x)$ will be $[x|x\neq \frac{\pi }{2} +\pi n]$ and $(- \infty,\infty),[y|y\in R]$ respectively.