Question

If f(x) = f(-x), then f(x) is called an even function. Which of the following are even functions?
1)f(x) =x^-2
2)f(x)=x^4
3)f(x)=2x^3

Answer 1

@ganeshie8 @mathmath333

Answer 2

plug in values.

Answer 3

example: \(f(2) = (2)^2 = ~?\), \(f(-2) = (-2)^22 = ~?\)

Answer 4

ahaha typo.

Answer 5

\[f(-2) = (-2)^2 = ~?\]

Answer 6

\(\large\tt \begin{align} \color{black}{f(x)=x^{-2}-----\color{red}{(1)}(given)\\~\\
f(-x)=(-x)^{-2}\\~\\
f(-x)=\dfrac{1}{(-x)^{2}}\\~\\
f(-x)=\dfrac{1}{(x)^{2}}\\~\\
f(-x)=(x)^{-2}-----\color{red}{(2)}\\~\\~\\
f(x)=f(-x)
}\end{align}\)

Answer 7

\(f(x) = x^{-2}\) we have \(f(-x)=\frac{1}{(-x)^2}=\frac{1}{x^2}=f(x)\)

Answer 8

so is it just the first one

Answer 9

no

Answer 10

No guessing >:o

Answer 11

I don't quite get how it wokrs

Answer 12

@Jhannybean

Answer 13

u have to substitute \(-x\) for \(x\) and see if
\(f(x)=f(-x)\)

Answer 14

^^^^

Answer 15

refer this
http://www.mathsisfun.com/algebra/functions-odd-even.html

Answer 16

"x" is just a value, a number, all you have to do is plug in a number.

Answer 17

I still don't know how it works, how should I approach this

Answer 18

So in functions that have an odd exponent, if you plug in a negative value for x, you will get a negative result. Example : \((-1)^{3} = (-1)(-1)(-1) = -1\)

Answer 19

so can u take me through one answer option by showing me if it is or isn't

Answer 20

If the polynomial has only even powers (+/-), it is an even function,
if the polynomial only has odd powers (+/-), it is an odd function.

Answer 21

\(\large\tt \begin{align} \color{black}{f(x)=x^{4}-----\color{red}{(1)}(given)\\~\\
f(-x)=(-x)^{4}\\~\\
f(-x)=(-1)^4(x)^{4}\\~\\
f(-x)=(1)x^{4}\\~\\
f(-x)=x^{4}-----\color{red}{(2)}\\~\\
\color{red}{(1)=(2)}\\~\\
f(x)=f(-x)\\
even
}\end{align}\)

Answer 22

ok ive worked out the third is odd am I right?

Answer 23

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