Find the Domain y=tg(x-pi/6)

Problem

y=tan(x−π/6)

Solution

1. Identify the restriction for the tangent function. The function tan(θ) is undefined whenever its argument θ is an odd multiple of π/2

2. Set up the inequality for the domain by stating that the argument of the tangent function cannot equal these values.

θ≠π/2+n*π

3. Substitute the specific argument from the given function into the inequality.

x−π/6≠π/2+n*π

4. Solve for x by adding π/6 to both sides of the inequality.

x≠π/2+π/6+n*π

5. Simplify the constant terms by finding a common denominator.

(3*π)/6+π/6=(4*π)/6=(2*π)/3

6. State the final condition for x where n represents any integer.

x≠(2*π)/3+n*π

Final Answer

Domain:{[x∈ℝ,x≠(2*π)/3+n*π,n∈ℤ]}

Want more problems? Check here!