Question

Which equation represents a tangent function with a domain of all Real numbers such that x ≠ π + 2πn, where n is an integer?

f (x) = tan(2x – π)
g(x) = tan(x – π)
h of x equals tangent of the quantity x minus pi over 2 end quantity
j of x equals tangent of the quantity x over 2 minus pi end quantity

Answer 1

The equation that represents a tangent function with a domain of all real numbers such that $x\ne \pi +2\pi\cdot n$ is $y = \tan \frac{x}{2}$.

How to analyze a trigonometric function

A tangent function is a trigonometric function whose domain contains the following set:

$Dom \{y\} = \mathbb {R}-\left\{\frac{\pi}{2}+\pi\cdot n|n\in \mathbb{Z} \right\}$

If we have a function of the form $y = \tan ax$, where $a$ is real number, then we must observe the following condition:

$\frac{\pi}{2}+\pi\cdot n = a\cdot \left(\pi + 2\pi\cdot n\right)$

And the value of $a$ is:

$a = \frac{1}{2}$

Hence, the equation that represents a tangent function with a domain of all real numbers such that $x\ne \pi +2\pi\cdot n$ is $y = \tan \frac{x}{2}$. $\blacksquare$

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