Chapter 3: Q. 12 (page 176)

Is the function $f (x) = \frac{x^{2}}{2 x + 1}$ even, odd, or neither?

Short Answer

Expert verified

The function is neither even nor odd.

Step by step solution

Step 1. Given information.

Is the function $f (x) = \frac{x^{2}}{2 x + 1}$ even, odd, or neither?

Step 2. Definition.

If the function is even then:

$f (- x) = f (x)$

If the function is odd then:

$f (- x) = - f (x)$

Step 3. Determine the function.

$f (x) = \frac{x^{2}}{2 x + 1} f (- x) = \frac{{(- x)}^{2}}{2 (- x) + 1} = \frac{x^{2}}{- 2 x + 1} = - \frac{x^{2}}{2 x - 1}$

So, $f (- x) \neq f (x) and f (- x) \neq - f (x)$ .

The function is neither even nor odd.

Step 3. Conclusion.

The function is neither even nor odd.

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Is the function $f (x) = \frac{x^{2}}{2 x + 1}$ even, odd, or neither?

Short Answer

Step by step solution

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Step 2. Definition.

Step 3. Determine the function.

Step 3. Conclusion.

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Is the function $f (x) = \frac{x^{2}}{2 x + 1}$ even, odd, or neither?