Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let f (x) = (x 12 − x 9 + x 4 − x + 1) − 1/2 . The domain of the function is :
Text Solution
Verified by ExpertsThe correct answer is:
D
( − ∞ , ∞ )
Sol. f(x) = (x 12 – x 9 + x 4 – x + 1) –1/2
Dr : x 12 – x 9 + x 4 – x + 1 > 0
For x ≤ 0 it is obvious that for f(x) to be defined Dr > 0.
For x ≥ 1, (x 12 – x 9 ) + (x 4 – x) + 1 is positive
Since x 12 ≥ x 9 , x 4 ≥ x.
For 0 < x < 1, Dr = x 12 + (x 4 – x 9 ) + (1 – x) > 0
Since x 4 > x 9 , x < 1.
Hence Dr > 0 for all x ∈ R
Domain is x ∈ R
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