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Chapter 2: Q.37 (page 90)

Determine algebraically whether each function is even, odd, or neither.

Fx=x3

Short Answer

Expert verified

Fxis an odd function.

Step by step solution

01

Given information.

The function,Fx=x3

02

Write definition of even function and odd function.

  • A function fxis said to be an even function if f-x=fx.
  • A function fxis said to be an odd function iff-x=-fx.
03

Calculate F-x.

Replace xby -xinto the given function Fx=x3.

localid="1646156332570" F-x=-x3=-x3=-Fx

Clearly, F-x=-Fx

So, by definition: Fxis an odd function.

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Most popular questions from this chapter

A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.

(a) Express the area A of the rectangle as a function of the radius r of the semicircle.

(b) Express the perimeter p of the rectangle as a function of r.

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.
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True or False Every relation is a function.

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A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

True or False

The graph of y=-f(x)is the reflection about the x-axis of the graph of y=f(x).
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