The domain of cos−1x−32−log10(4−x) is
The domain of cos−1x−32−log10(4−x) is
let cos−1x−32=θ⇒cosθ=x−32
−1≤cosθ≤1
−1≤x−32≤1
−1≤x−32≤1
−2≤x−3≤2
−2+3≤x≤2+3
1≤x≤5
So, 1≤x≤5⟶(1)
log10(4−x)
as log is only defined for positive numbers
4−x>0
4>x⟶(2)
Taking intersection on both (1) and (2)
We get
1≤x<4 or x∈[1,4)