Domain and range.

3) If f(x) = √(1 - x) and g(x) = log_ex are two real functions, then describe functions

fog and gof.

Please teach me to find out the range and domain, achchhe se [1]

Thanks in advance [1]

3)

fog=√(1-lnx)

now domain of f is (-∞,1)

domain of g is (0,∞)_

so domain of fog is intersection of these 2 which is (0,1)

now range is as x approaches 0 , ln x tends to -∞ and as x approaches 1 , ln x tends to 0

so range will be (0,∞)

3) gof =ln(√1-x)

now √1-x is always greater than 0 when x <1

sop domain is (-∞,1)

range is (-∞,∞)

1) its pretty obvious

f(x0=√x-2

f(f(x))=√√(x-2) -2

so for this to be valid √x-2 >2

so x>6

and continue so on

2)

left it so that u could give a try

fog=√(1-tan²x)

for this to be valid tan²x<1 implies from the given domain of f , for this inequality to be satisfied, we have

x belongs to (-Î /4,Î /4)U(-3Î /4,3Î /4)

and range as we can see is (0,√2)

similarly try for gof

you shud practice these chapters frm a standard book

well, these seek basic common sense and if u arent able to do

i suggest u once again go through ncert text bo