Find Where Undefined/Discontinuous f(x)=tan((pix)/2)

Problem

ƒ(x)=tan((π*x)/2)

Solution

1. Identify the condition for the tangent function to be undefined. The function tan(θ) is undefined when its argument θ is an odd multiple of π/2

2. Set up the equation for the undefined points by setting the argument of the tangent function equal to the general form of odd multiples of π/2

(π*x)/2=((2*k+1)*π)/2

3. Solve for x by multiplying both sides of the equation by 2/π to isolate the variable.

x=2*k+1

4. Define the set of values for k Since k represents any integer, the function is undefined and discontinuous at all odd integers.

k∈ℤ

Final Answer

x=2*k+1,k∈ℤ

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