Let f : R R be defined by f ( x ) = x 2 - 8 x 2 + 2 , then f is:

Question

Let $f : R \to R$ be defined by $f (x) = \frac{x^{2} - 8}{x^{2} + 2},$ then $f$ is:

Smart Achievers · Accepted Answer

(4)

Ans. Neither one-one nor onto

Explanation:

Given, $f (x) = \frac{x^{2} - 8}{x^{2} + 2},$

$f$

$f (- 3) = \frac{9 - 8}{9 + 2} = \frac{1}{11}$

Here, $f (3) = f (- 3)$ but $3 \neq - 3$ .

$\Rightarrow f$ is not one-one.

Now, $f (x) = \frac{x^{2} - 8}{x^{2} + 2} = 1 - \frac{10}{x^{2} + 2}$

So, minimum value of $f (x) = 1 - 5 = - 4$

$∴$ It is not onto.

Hence it is neither one-one nor onto.

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