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Chapter 2: Q. 20 (page 124)

Determine(algebraically)whethere the given function is even, odd,or neither.

G(x)=1-x+x2

Short Answer

Expert verified

The given functionG(x)=1-x+x2is neither even nor odd.

Step by step solution

01

Step 1.Given information

The given function G(x)=1-x+x2

02

Step 2. Determine the given function is even,odd or neither

The function is even if G(-x)=G(x)and odd if G(-x)=-G(x).If none of these conditions are satisfied.

Find G(-x) by replacing -x forx in the given function.
G(-x)=1-(-x)+(-x)3=1+x-x3

We can see that G(-x)≠G(x)andG(-x)≠-G(x).Therefore the given function is neither even nor odd

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