Q.
If f(x)=3∣x∣−x−2 and g(x)=sinx, then domain of f∘g(x) is
420
120
Relations and Functions - Part 2
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Solution:
f(g(x))=3∣sinx∣−sinx−2 ∴3∣sinx∣−sinx−2≥0 sinx>0sinx<0 sinx≥1 sinx≤(−21) ⇒sinx=1 x=2mπ+2π,m∈I ......(i) x∈[67π,611π]⇒x∈[2nπ+67π,2nπ+611π],n∈I....(ii) ∴ Union of (i) and (ii) is the domain of fog(x).