UPSEE Solved Model Paper 7

Let f (x) = x12−x9+x4−x+1
= (x9+x)(x3−1) + 1 > 0 for all x ≥ 1 ... (i)
Again, f (x) = x4(x8+1)−x(x8+1)+1
= x(x8+1)(x3−1) + 1 > 0 for all x ≤ 0 ... (ii)
Next f (x) = x12+x4(1−x5) + (1 - x) > 0 for all 0 < x < 1 ... (iii)
Combining Eqs. (i), (ii), (iii) we get
x ∊ (- ∞ , ∞)