anonymous
  • anonymous
How do I express the following in terms of a function of x: sin(x)=e^(-x) ?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
f(x)=sinx-e^(-x)
amistre64
  • amistre64
im not sure if that function expresses the equality between them, so you might need to say something regarding the roots of it; when f(x)=0
anonymous
  • anonymous
@amistre64 but he posted it as an equality and i think if we draw there graphs we will see there there will be n number of roots.So roots won't be meaningfull

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amistre64
  • amistre64
im not sure one way over the other :) just a gut feeling
anonymous
  • anonymous
@godfreysown yes equate it to zero
anonymous
  • anonymous
so why is it that this simple manipulation turns an equation into a function of x? (PS: I've attached a graph of your f(x) )
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amistre64
  • amistre64
a relation is roughly defined as any interaction or change in output resulting from input \[g(a) = {b_1,b_2,b_3,...}\]there need not be any unique answer. This is not very useful when we are trying to make predictions about how something will react. a function is a special kind of relation and is defined as an equation that has only one output value (its unique) for any given input value. \[f(a) = b\]as such, we can use these to determine past and future, as well as present outputs from a system that can be modeled by functions
amistre64
  • amistre64
if 2 things are equal; then subtracting one from the other leaves us with nothing. To determine when: sin(x)=e^(-x) , we can subtract one from the other and determine at what values of "x" the function equals zero. also, since e^(-x) never equates to zero on its own; we can divide it out instead\[f(x)=\frac{sin(x)}{e^{-x}}=e^{x}~sin(x)=1\] \[f(x)=e^{x}~sin(x)-1 =0\]
anonymous
  • anonymous
@amistre64 haven't u complicated the equation, i would always prefer to solve f(x)=sinx-e^(-x) rather than f(x)e^x sinx-1
amistre64
  • amistre64
it asked for a function; complication wasnt specified :)
anonymous
  • anonymous
@amistre64 he he nice one :), but tasks of using maths is to always make things simple, isn't it i guessed it that way or may be is is not
amistre64
  • amistre64
most maths are done on computers these days, and a computer has no concept of simple. What might relate is "number" of computations required in which you would want to streamline it to reduce the number of steps that a computer would have to take for it.
amistre64
  • amistre64
ive got no idea which function between ours would be "simpler" for a computer tho
anonymous
  • anonymous
@amistre64 agreed :) , i think you are a mod , i have mailed at abuse@openstudy.com to delete my account , can u help in this.Also i have posted in openstudy feedback
amistre64
  • amistre64
i dont have the abilities to alter accounts.
amistre64
  • amistre64
..and i dont have any pull in that area either ... thats under the operations of the administrators

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