Solve for x, f(x)=1÷(2-4cos2x)

Question

Given (0;2) is the function discontinuous

Answer 1

f(x)=1/(2-4cos(2x)) has a discontinuity when the denominator is zero.

Assuming you mean the interval [0,2π], 4cos(2x)=2 at the discontinuity.

So cos(2x)=½, 2x=π/3 or 60º, so x=π/6 (30º).

But cos(2x)=½ when 2x=2π-π/3=5π/3 (300º). So x can also be 5π/6 (150º). Between π/6 and 5π/6 it’s continuous.