If a function is defined as f(x) = 
, where g(x) = |sinx| + sinx , h(x) = sinx + cosx , 0 ≤ x ≤ π .Then find the doman of f(x).
Text Solution
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Sol. (i) g(x) > 0 ⇒ |sinx | + sinx > 0 ⇒ 0 < x < π ................
(ii) 0 < h(x) <1 or h(x) > 1
0 < sinx + cosx < 1 ⇒ 
................
sinx + cosx >1 ⇒ 
..................
(iii) log h(x) g(x) ≥ 0
since h(x) > 1, g(x) ≥ 1
i.e. |sinx| + sinx ≥ 1 ⇒ sinx ≥ 
, ( sinx > 0) ⇒ 
................
From and 
0 < h(x) < 1 then 0 < g(x) ≤ 1
0 < |sinx| + sinx ≤ 1 ⇒ 
i.e. 
............... (E)
From B & E x ∈ φ so final domain is 
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