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Chapter 2: Q. 33 (page 90)

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

f(x)=4x3

Short Answer

Expert verified

fxis an odd function.

Step by step solution

01

Given information.

The functionf(x)=4x3.

02

Write definition of even function and odd function.

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

Calculate f-x.

Replace xby -xinto the given function fx=4x3.

f-x=4-x3=-4x3=-fx

As, f-x=-fx

So, by definition: fxis an odd function.

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Most popular questions from this chapter

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

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