The values of x where the function f(x)=tan⁡xlog⁡(x−2)x2−4x+3 is discontinuous are given by

f(x)=tan⁡xlog⁡(x−2)x2−4x+3, being product and quotient of functions tan⁡xlog⁡(x−2) and x2−4x+3 must be continuous in its domain of definition. tan⁡x is discontinuous in {(2n+1)π/2:n∈Z}log⁡(x−2) discontinuous for x≤2 and x2−4x+3=0 for x=1 and 3.  Hence f(x) is discontinuous in [−∞,2]∪{3,nπ+π/2:n∈Z}[−∞,2]∪{3,nπ+π/2:n≥1}Hence (3) is the correct answer.