Question

the domain of the function fx=√logx^2-1x​

Answer 1

Step-by-step explanation:

f(x)=logx(cos2πx)

i) log is defined when its base x>0 and x=1

ii) and cos2πx>0⇒2πx>(2n+1)2π⇒x>4(2n+1)

iii) Square roots is defined when logx(cos2πx)≥0

⇒cos2πx≥1⇒2πx≥2nπ⇒x≥n

Therefore from (i),(ii) and (iii) we get

(0,41)∪(43,1)∪{x:x∈N,x≤2}