Question

Which functions are even? Select all that apply

Answer 1

Options B, C and E are even functions.

Explanation:

If f(x) = f(-x) then function is called to be even.

A). f(x) = ∛8x

f(-x) = ∛8(-x) = (∛8)(∛(-x) = 2∛(-x)

Therefore f(x) ≠ f(-x)

So function is not an even function.

B).
`f(x)=log_(9)x^(6)`

`f(-x)=log_(9)(-x)^(6)`

`=log_(9)(x)^(6)`

f(x) = f(-x)

So this function is even.

C).
`f(x)=(1)/(x^(8)+7x^(7))`

`f(-x)=(1)/((-x)^(8)+7(-x)^(6))`

=
`(1)/(x^(8)+7x^(6))`

f(x) = f(-x)

Therefore given function is even.

D). f(x) =
`e^{x^(8)-x }`

`f(-x)=e^{(-x)^(8)-(-x)}=e^{x^(8)+x}`

Therefore f(x) ≠ f(-x)

So the given function is not even.

E). f(x) = |8x| - 3

f(-x) = |8(-x)| - 3

= |8x| - 3

f(x) = f(-x)

Therefore, function is even.

F).
`f(-x)= -9(-x)^(10)+5(-x)^(4)-12(-x)`

`f(-x)= -9(x)^(10)+5(x)^(4)+12(x)`

f(x) ≠ f(-x)

Therefore the given function is not an even function.

Options B, C and E are even functions.

Answer 2

The even functions are options 2, 3, and 5

Explanation:

Please, see the attached file.

Thanks.