1Not [ ] represents greatest integral function.
Find the domain of the following:-
(a) F(x) = sin -1{ (2-3[x] ) / 4 }
(b) F(x) = sin |x| + sin -1 (tanx) + sin (sin -1 x)
(c) F(x) = (x 2 - |x| - 2) 1/2
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7 Answers
62(a) F(x) = sin -1{ (2-3[x] ) / 4 }
so -4≤ 2-3[x] ≤4
or -4≤ 3[x]-2 ≤4
or -2≤ 3[x] ≤6
or -2/3≤ [x] ≤2
which is true for 0 ≤ x < 3
11Soln
b)
First find the domain of each function and then find the intercept of that.
Sin |x| is (-∞,∞)
Sin-1tan x [-pi/4,pi/4] this the fundamental Doamin
SinSin-1x [-1,1]
Therefore the intercept is [-pi/4,pi/4]
11Soln
c)
(x2 -|x|-2)1/2
For x>0
(x2 -x-2)1/2
√(x-2)(x+1)
Domain [2,∞)
For x<0 x = -x
(x2 +x - 2)1/2
√(x+2)(x-1)
Domain for -x is [1,∞)
For x is (-∞,-1]U[2,∞)
3think it shud be (-infinity,-2] union (inf,2]
put -1 it dosnt satify virag!!!!!!!!!!!!!