Question

another desperate attempt :(...
Find the inverse of the following function. Find the domain, range, and asymptotes of each function. Graph both functions on the same coordinate plane. f ( x ) = 12 e^ − x

Answer 1

can you draw that , more or less?

Answer 2

i mean , the function \(f(x)=12e^{-x}\)

Answer 3

honestly i dont even konw what it is :(

Answer 4

It is an exponential decay fn.

Answer 5

For finding inverse of a function you always interchange x and y and then solve for y

Answer 6

\[f(x) = y = 12e ^{-x}\]Now interchange x and y \[x = 12e ^{-y} \]\[\frac{ x }{ 12 } = e ^{-y}\]\[\ln (\frac{ x }{ 12 }) = \ln e ^{-y}\]\[\ln (\frac{ x }{ 12 }) = -y \]\[y = - \ln (\frac{ x }{ 12 })\]

Answer 7

Given a function \(f\), that sends an \(x\) onto a \(y\), and if this function creates a one-to-one correspondance between a set of numbers \(x\) and another set of numbers \(y\), people try to find the correspondance between \(x\) and \(y\) in the "other direction".

easy example: \(f(x)=2x\). So \(x\) and \(2x\) are in correspondance. the quantity \(2x\) is one of the \(y\)'s.. This correspondance gives \(y\) in terms of \(x\).
To find the correspondance in the other direction, you isolate \(x\) in order to have the expression of \(x\) given \(y\).
-> \(y=2x\) ->\(x=y/2\). So, the function that sends a \(y\) on \(y/2\) is called the reciprocal function.

Answer 8

another example: \(f(x)=x^3\).
isolate \(x\) in the relation \(y=x^3\):
\(x=\sqrt[3]{y}\). the function \(g(y)=\sqrt[3]y\) is the reciprocal function of \(f\).

Answer 9

so, the guy rajee_sam did what i explained. he wrote the relation \(y=f(x)=12e^{-x}\), and he isolated the variable \(x\). (at the end he switched the role of \(x\) and \(y\) betcause he prefers it like that. no need tho).