Login

If f(x) = sqrt ( | 3^x - 3^(1-x) | - 2) and g(x) = tan (pi*x) then domain of fog(x) is

Dear student,
fx=3x-33x-2, gx=tanπxfor domain of fx 3x-33x-2≥03x-33x≥2let 3x=t and t>0 ...1-2≥t-3t≥2i) t-3t≥2t2-2t-3≥0t-3t+1≥0then -1≥t≥3 ...2ii) -2≥t-3tt2+2t-3≤0t+3t-1≤0then -3≤t≤1 ....3using eq1,eq2 and eq3 -1≥t≥3∪-3≤t≤1∩t>0then solution  0<t≤1,t≥3put t=3x0<3x≤1,3x≥3then domain of fx-∞<x≤0,x≥1x∈(-∞,0]∪[1,∞)then domain of fgx-∞<gx≤0,gx≥1-∞<tanπx≤0,tanπx≥1-π2-nπ<πx≤-nπ,nπ+π2≥πx≥nπ+π4-12-n<x≤-n,n+12≥x≥n+14 where n=0,1,2,3.....
Hope this information will clear your doubts. If you have any more doubts just ask here on the forum and our experts will try to help out as soon as possible.
Regards

  • 0
View Full Answer
What are you looking for?