CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let f(x) = x² − 4x + 7 be defined on R. Which statement is correct?
f is many-one. Writing f(x) = (x − 2)² + 3 shows that f(1) = f(3) = 4 for different inputs, so it is not one-one. It is also not onto R because values below 3 are never reached.
- Af is one-one
- Bf is an even function
- Cf is many-oneCorrect
- Df is onto R
Explanation
f(x) = (x − 2)² + 3, so f(1) = 4 and f(3) = 4 with 1 ≠ 3. Hence f is many-one. It is not onto R since its minimum value is 3. It is not even because f(−1) = 12 while f(1) = 4.
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