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Chapter 2: Q.39 (page 90)

Determine algebraically whether each function is even, odd, or neither.
$f (x) = x + |x|$

Short Answer

Expert verified

$f (x)$ is neither even nor odd function.

Step by step solution

01

Given information.

The function, $f (x) = x + |x|$ .

02

Write definition of even function and odd function.

A function $f (x)$ is said to be an even function if $f (- x) = f (x)$ .
A function $f (x)$ is said to be an odd function if $f (- x) = - f (x)$ .

03

Calculate f-x.

Replace $x$ by $- x$ into the function $f (x) = x + |x|$ .

$f (- x) = - x + |- x| = - x + |x|$

Clearly, $f (- x) \neq f (x) a n d f (- x) \neq - f (x)$

So, by definition: $f (x)$ is neither even nor odd function.

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If the domain of $f$ is all real numbers in the interval $[0, 7]$ and the domain of g is all real numbers in the interval $[- 2, 5]$ , the domain of $f + g$ is all real numbers in the interval _________.

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