Q78.Let f : A → B be a function defined as f(x) = x−1x−2 , where A = R −{2} and B = R −{1}. Then f is (1) invertible and f −1(y) = 2y+1y−1 (2) invertible and f −1(y) = 3y−1y−1 (3) no invertible (4) invertible and f −1(y) = 2y−1y−1 1 −1) 2−x , x > 1, x ≠2
What This Question Tests
This question requires determining if a given function is invertible by checking its domain, codomain, and properties (injectivity and surjectivity), and then correctly calculating its inverse function.
Concepts Tested
Formulas Used
y = f(x) => x = f⁻¹(y)
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📋 Question Details
- Chapter
- Sets Relations Functions
- Topic
- Invertible functions and inverse
- Year
- 2018
- Shift
- 15 Apr Shift 2 Online
- Q Number
- Q78
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 1: Relations & Functions
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