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If f:ℕ→ℝ is a...

Question

If $f : N \to R$ is a function defined as $f (x) = 2 x^{2} + 1$ , then the preimage of $9$ is

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Solution

Here, $f (x) = 2 x^{2} + 1$
$f (x) = 9$
$\Rightarrow 9 = 2 x^{2} + 1$
$\Rightarrow 8 = 2 x^{2}$
$\Rightarrow 4 = x^{2}$
$\Rightarrow x = - 2, 2$
But $x \in N$
$∴ x = 2$
Preimage of $9$ is $2.$

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