FunctionHard
Question
Let f(x) = (x12 - x9 + x4 - x + 1)-1/2. The domain of the function is :
Options
A.(1, ∞)
B.(- ∞ , - 1)
C.(- 1 , 1)
D.(- ∞ , ∞)
Solution
f(x) = (x12 - x9 + x4 - x + 1) -1/2
Dr : x12 - x9 + x4 - x + 1 > 0
For x ≤ 0 it is obvious that for f(x) to be defined Dr > 0.
For x ≥ 1, (x12 - x9) + (x4 - x) + 1 is positive
Since x12 ≥ x9, x4 ≥ x.
For 0 < x < 1, Dr = x12 + (x4 - x9) + (1 - x) > 0
Since x4 > x9, x < 1.
Hence Dr > 0 for all x ∈ R
Domain is x ∈ R
Dr : x12 - x9 + x4 - x + 1 > 0
For x ≤ 0 it is obvious that for f(x) to be defined Dr > 0.
For x ≥ 1, (x12 - x9) + (x4 - x) + 1 is positive
Since x12 ≥ x9, x4 ≥ x.
For 0 < x < 1, Dr = x12 + (x4 - x9) + (1 - x) > 0
Since x4 > x9, x < 1.
Hence Dr > 0 for all x ∈ R
Domain is x ∈ R
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