hm this is hard
if a function f(x) is mapping x to y, then the inverse function f(x) maps y back to x
\(y=\frac{15}{1+4e^{-0.2x}}\)
interchange the variables x and y
\(x=\frac{15}{1+4e^{-0.2y}}\) solve for y
\(y=-5\ln \left(\frac{-x+15}{4x}\right)\)
\(-5\ln \left(\frac{-x+15}{4x}\right)\)
find the domain of each inverse function
domain of \(v\begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:
the domain of a function is the set of input or argument values for which the function is real and define
find positive values for log \(0
\(\log _af\left(x\right)\quad \Rightarrow \quad \:f\left(x\right)>0\)
\(\frac{-x+15}{4x}>0\)
multiply both sides by 4
\(\frac{4\left(-x+15\right)}{4x}>0\cdot \:4\)
simplify:
\(\frac{-x+15}{x}>0 \)
x<0 | X=0 | 0 | x=15 | x>15 | |
-x+15 | + | + | + | 0 | _ |
x | - | 0 | + | + | + |
-x+15/x | - | undefined | + | 0 | - |
OMG i cant do this anymore
srry , thats all i know