CUET · MATHS · PYQ PAPER 2023
If a function \(f: R \rightarrow R\) is defined by \(f(x)=x^2+1\), then the pre-images of 17 and -3 respectively are:
- A \(\varnothing,\{4,-4\}\)
- B \(\{3,-3\}, \varnothing\)
- C \(\{4,-4\}, \varnothing\)
- D \(\{4,-4\},\{2,-2\}\)
Answer & Solution
Correct Answer
(C) \(\{4,-4\}, \varnothing\)
Step-by-step Solution
Detailed explanation
For pre-images of 17: \(x^2 + 1 = 17\) \(x^2 = 16\) \(x = \pm 4\) Pre-images of 17 are \(\{-4, 4\}\). For pre-images of -3: \(x^2 + 1 = -3\) \(x^2 = -4\) No real solutions, so pre-images of -3 are \(\varnothing\).
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