Answer to Question #220217 in Calculus for tttt

Question #220217

𝑓(π‘₯) = 𝑒 βˆ’π‘₯ 1+π‘’βˆ’π‘₯ . i) Determine whether 𝑓(π‘₯) is a one-to-one function. 


1
Expert's answer
2021-07-27T10:57:10-0400

Let's solve the equation f(x)=f(y)f(x)=f(y) :

eβˆ’x1+eβˆ’x=eβˆ’y1+eβˆ’y\frac{e^{-x}}{1+e^{-x}}=\frac{e^{-y}}{1+e^{-y}}

1ex+1=1ey+1\frac{1}{e^x+1}=\frac{1}{e^y+1}

ex+1=ey+1e^x+1=e^y+1

ex=eye^x=e^y

x=yx=y

This means that the function f(x)f(x) is one-to-one.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment