Question

Give an example of an even function and explain algebraically why it is even.

Answer 1

So, an even function \(f\) is a function where for all \(x\), \(f(x) = f(-x)\). The square function and the absolute-value functions are pretty cool examples.

Answer 2

is that it?

Answer 3

Maybe.

Answer 4

Do you know what \(|x|\) is?

Answer 5

x

Answer 6

And \(|-x|\).

Answer 7

x

Answer 8

Bang on!

Answer 9

And do you know what \((-x)^2\) is?

Answer 10

x?

Answer 11

Nope

Answer 12

o

Answer 13

x^2

Answer 14

Yes.

Answer 15

That's correct! =)

Answer 16

so how does that answer this question, bro? :)

Answer 17

You just answered the question, “explain algebraically why it is even”.
Look back at the definition.

Answer 18

If

f(-a)=f(a) then it is even

example

f(x)=x^2

f(-x)=(-x)^2
f(-x)=x^2

therfore,

f(x)=f(-x)


@parth explained it well :)

Answer 19

@ParthKohli *

Answer 20

:)

Answer 21

Let me do that for an absolute-value function too! So we define the absolute value function as follows\[f(x) = \cases{x \ \ \text{iff} \ \ x >0 \\ -x \ \ \text{iff} \ \ x < 0 }\]It is clear that \(f(-x)=f(x)=x\), hence an even function.