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Chapter 2: Q. 35 (page 90)

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

gx=-3x2-5

Short Answer

Expert verified

gxis an even function.

Step by step solution

01

Given information.

The function:gx=-3x2-5

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 if f-x=-fx.
03

Calculate g-x.

Replace xby -xinto the given function gx=-3x2-5.

g-x=-3-x2-5=-3x2-5=gx

As, g-x=gx

So by definition,gxis an even function.

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