Awesomegirl2003
Awesomegirl2003 Awesomegirl2003
  • 17-03-2020
  • Mathematics
contestada

Prove algebraically what type of function this is (even, odd, or neither).

Prove algebraically what type of function this is even odd or neither class=

Respuesta :

shilpa85475 shilpa85475
  • 25-03-2020

The given function is even.

Solution:

Given function:

[tex]f(x)=x^{6}-x^{4}[/tex]

If f(-x) = -f(x), then the function is odd.

If f(-x) = f(x), then the function is even.

[tex]f(x)=x^{6}-x^{4}[/tex]

Substitute x = -x

[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]

          [tex]=x^{6}-x^{4}[/tex]

          = f(x)   (given)

   f(-x) = f(x)

From the definition, it is even.

Hence the given function is even.

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