CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The domain of the function f(x) defined by
f(x)=1log10(2x)+x+2 is

A
(2, 1)(1, 2)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[2, 2]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
[2, 1)(1, 2]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
[2, 1)(1, 2)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D [2, 1)(1, 2)
We havef(x)=1log10(2x)+x+2Let g(x)=1log10(2x) and h(x)=x+2Thus, f(x)=g(x)+h(x)Domain (f)=Domain (g(x)) Domain (h(x))Now, g(x)=1log10(2x) is defined for all x for which log10 (2x) is defined and log10(2x)02x>0 and 2x1x<2 and x1x(, 1)(1, 2)Domain (g) =(, 1)(1, 2)And, h(x)=x+2 is defined for all x satisfying,x+20x2x[2, ).Domain (h) =[2, )Hence, Domain (f)={(, 1)(1, 2)}[2, ) Domain (f)=[2, 1)(1, 2)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Animalia
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon