Q77 / 180 · KCET 2024 · Mathematics
Let $f: R \rightarrow R$ be defined by $f(x)=x^2+1$. Then, the pre images of 17 and -3 . respectively are
- A$\phi,\{4,-4\}$
- B$\{3,-3\}, \phi$
- Correct answerC$\{4,-4\}, \phi$
- D$\{4,-4\},\{2,-2\}$
Solution
$\because$ For pre image of 17 , we have
$f(x)=x^2+1=17$
$\Rightarrow \quad x^2=16 \Rightarrow x= \pm 4$
So, $x \in\{-4,4\}$
For pre image of -3 , we have
$f(x)=x^2+1=-3$
$\Rightarrow \quad x^2=-4($ not possible $)$
Hence, no possible pre image.
Hence, the correct answer is option: 'C'.