Find the Domain y=3tan(2x)

Problem

y=3*tan(2*x)

Solution

1. Identify the restriction for the tangent function. The function tan(θ) is undefined where its input θ results in a vertical asymptote, which occurs at θ=π/2+n*π for any integer n

2. Set up the inequality for the given expression. In the function y=3*tan(2*x) the input to the tangent function is 2*x Therefore, we must have:

2*x≠π/2+n*π

3. Solve for x by dividing all terms by 2

x≠π/4+(n*π)/2

4. State the domain in set-builder notation, where n represents any integer.

Final Answer

Domain: *{x|x≠π/4+(n*π)/2,n∈ℤ}

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