How do I express the following in terms of a function of x: sin(x)=e^(-x)
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Question

How do I express the following in terms of a function of x: sin(x)=e^(-x)
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anonymous · Answer

f(x)=sinx-e^(-x)

amistre64 · Answer

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 · Answer

@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

amistre64 · Answer

im not sure one way over the other :)  just a gut feeling

anonymous · Answer

@godfreysown yes equate it to zero

anonymous · Answer

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) )

amistre64 · Answer

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 · Answer

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 · Answer

@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 · Answer

it asked for a function; complication wasnt specified :)

anonymous · Answer

@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 · Answer

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 · Answer

ive got no idea which function between ours would be "simpler" for a computer tho

anonymous · Answer

@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 · Answer

i dont have the abilities to alter accounts.

amistre64 · Answer

..and i dont have any pull in that area either ... thats under the operations of the administrators