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Chapter 2: Q 43. (page 90)

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.

h(x)=-x33x2-9

Short Answer

Expert verified

The given functionh(x)=-x33x2-9is an odd function.

Step by step solution

01

Step 1. Write the given information and use the definition of odd and even function.

The given function is:

h(x)=-x33x2-9

A function fis even if, for every number xin its domain, the number -xis also in the domain and f(-x)=f(x).

A function fis odd if, for every numberxin its domain, the number -xis also in the domain andf(-x)=-f(x).

02

Step 2. Determine if the function is even.

Replace xby -xin the given function,

h(-x)=-(-x)33(-x)2-9=-(-x)33(x)2-9=x33x2-9

Sinceh(-x)鈮�h(x),his not an even function.

03

Step 3. Determine if the function is odd.

Find the function -h(x),

role="math" localid="1645811470834" -h(x)=-(-x33x2-9)=x33x2-9

Sinceh(-x)=-h(x),his an odd function.

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