Question

Need a second opinion -
If f is an even function defined on the interval (-5,5), then find four real values of x satisfying the equation -

Answer 1

\[f(x) = f \left( \frac{ x+1 }{ x+2 } \right)\]

Answer 2

My answer -
\[\frac{ -1\pm \sqrt 5 }{ 2 } , \frac{ -3\pm \sqrt 5 }{ 2 }\]

Answer 3

Answer in the book -
\[\frac{ -3\pm \sqrt 5 }{ 2 } , \frac{ +3\pm \sqrt 5 }{ 2 }\]

Answer 4

Is that an even function?

Answer 5

Yes, f is an even function.

Answer 6

I thought "even" meant f(-x) = f(x), or have I gotten it wrong?

Answer 7

you got it right, doug

Answer 8

@douglaswinslowcooper
f satisfies f(-x) = f(x)

Now we need to find four values of x satisfying f(x) = f((x+1)/(x+2))

Answer 9

http://www.wolframalpha.com/input/?i=x+%3D+-%28x%2B1%29%2F%28x%2B2%29

Answer 10

how did u get the other two values ?

Answer 11

I used -
\[x = \frac{ x+1 }{ x+2 }\]

Answer 12

thats incorrect right ?

whenever (x, f(x)) is a point on graph,
then (-x, f(x)) will be a point also...

if x1 and x2 output the same value,
then
x1 = -x2

Answer 13

f(x1) = f(x2)
=>
x1 = -x2

Answer 14

im just messing wid the symmetry..

Answer 15

correct right, f(2) = f(-2) when f is even

2 = --2

Answer 16

If f is an even function; cant we say
f(x) = f(y) => x=±y
??

Answer 17

oh in this particular problem yes..
LastDayWork.. pls throw some light on how u got the other two values...

Answer 18

hmm no i dont think so :
cuz, if f(2) = f(3)
then 2 =/= +- 3

Answer 19

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

Answer 20

No, I mean for an even function f
If f(x) = f(y)
then x = y or x = -y

Answer 21

?