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Chapter 2: Q 41. (page 90)

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

g(x)=x2+3x2-1

Short Answer

Expert verified

The given functiong(x)=x2+3x2-1is even.

Step by step solution

01

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

The given function is:

g(x)=x2+3x2-1

A function fis even if, for every number localid="1645809152331" xin its domain, the number -xis also in the domain and f(-x)=f(x).

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

02

Step 2. Determine if the function is even.

Replace xby -xin the function:

g(x)=x2+3x2-1

g(-x)=(-x)2+3(-x)2-1=x2+3x2-1

Since h(-x)=h(x), the function is even.

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