Q2 / 87 · NTA Abhyas (JEE Main) 2020 · Mathematics · Functions

The domain of the function fx=x-1-x24 is

  • A
    -1,-12∪12,1
  • B
    -1,1
  • C
    -∞,-12∪12,∞
  • Correct answer
    D
    12,1

Solution

fx=x-1-x24
For fx to be real
x-1-x2≥0 and 1-x2≥0
⇒2x2-1≥0 and x2-1≤0
⇒x+12x-12≥0 and x+1x-1≤0
⇒x≤-12 or x≥12 and x∈-1,1
When x∈-1,-12, then x-1-x2 is negative
Hence, the required domain is 12,1

Hence, the correct answer is option: 'D'.

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