Question

Need your help. How can I determine an even and odd function?

Answer 1

take the given function,
put x = -x

if f(x) = f(-x), then its even
if (x) = -f(x), then its odd

if you dont get one of the above, then its neither even or odd.

Answer 2

can you give me some examples? @rsadhvika i really need to understand it

Answer 3

f(x) = x^2

Answer 4

test and see if its even or odd

Answer 5

f(x) = x^2

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


since, f(-x) = f(x), its an even function.

Answer 6

even?

Answer 7

yes, lets do another example :-

f(x) = x^3

Answer 8

odd ?

Answer 9

yes, one more :-

f(x) = x^2 + 1

Answer 10

even

Answer 11

actually no

Answer 12

aw.. ;'(

Answer 13

f(x) = x^2+1

put x = -x
f(-x) = (-x)^2 + 1
= x^2 + 1
= f(x)

Answer 14

you're right actually, im wrong, its even :)

Answer 15

i want to give u one example, which is neither even or odd. let me think...

Answer 16

okay ^^

Answer 17

try this :
f(x) = x^2+x

Answer 18

okay this is hard. Is it an odd?

Answer 19

f(x) = x^2+x

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

Answer 20

its neither f(x) or -f(x)

so its not even not odd.

Answer 21

how can you determine if the function is not even and odd?

Answer 22

f(x) = x^2+x

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

after doing above, lay back and look at what u got

Answer 23

u got x^2-x

x^2-x \(\ne\) f(x)

x^2-x \(\ne\) -f(x)

Answer 24

so its, not even, not odd

Answer 25

I see ! I get it now
Thank you @rsadhvika

Answer 26

:)

Answer 27

@rsadhvika now , how can you determine if the function is increasing or decreasing?

Answer 28

we need to look at graph