How do I find the domain and range of y=tan(2x-pi)?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The domain of a function y = f(x) is all the values that the independent variable x can take which gives real values for y.

The range is the values of y when x lies in the domain.

The tangent function is periodic with a periodicity of pi.

Here, y = tan (2x - pi)

For the set of values [-pi/2, pi/2], the value of the tangent of every angle can be found except -pi/2 and pi/2.

2x - pi cannot be equal to pi/2, 2x cannot be equal to 3pi/2, x cannot be equal to 3*pi/4

2x - pi cannot be equal to -pi/2, 2x cannot be equal to pi/2, x cannot be equal to pi/4

The domain of the function is R - {k*pi/4, -3*k*pi/4} where k is an integer.

The range of the function is R.

The required domain is R - {k*pi/4, -3*k*pi/4} and the range is R

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