Question
Find the formula for the inverse of the function
y =(e^x) / (1+8e^x)
y =(e^x) / (1+8e^x)
Answers
Reiny
to form the inverse , we interchange the x and y variables, so the inverse equation is
x = e^y/(1+8e^y)
now we have to solve that for y ....
e^y = x + 8x e^y
e^y - 8x e^y = x
e^y( 1 - 8x) = x
e^y = x/(1-8x)
y = ln(x/(1-8x) or lnx - ln(1-8x)
x = e^y/(1+8e^y)
now we have to solve that for y ....
e^y = x + 8x e^y
e^y - 8x e^y = x
e^y( 1 - 8x) = x
e^y = x/(1-8x)
y = ln(x/(1-8x) or lnx - ln(1-8x)
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