exponentials functions basics

Exponential
Functions

,Inverse function: Now, n
If we place 𝑥 in
We know that: The i
ln 𝑥
ln 𝑥 We get
𝑒 =𝑥
Is the
the 𝑥 ln 𝑥
initial 𝒙
𝑒𝑥 The i

Then if we place ln 𝑥 in …
Same happens here: Is the
𝑒𝑥
𝑥
ln 𝑒 =𝑥 We get
the 𝑥 𝑒𝑥
initial 𝒙
ln 𝑥

Thus: ln 𝑥 & 𝑒𝑥 are Inverse functions

, Inverse function:
Let 𝑓 be the function defined over an interval 𝐼 that associates to every antecedent 𝑥 a
𝑦 such that 𝑦 = 𝑓(𝑥).


𝑥 By 𝑓 𝑦
If 𝑓 is continuous and strictly monotone over 𝐼, then there exists a inverse function 𝑓 −
that 𝑓 −1 gives back the antecedents of 𝑓. That is why it is called an inverse function.


𝑦 By 𝑓 −1 𝑥
The function 𝑓, gives the images 𝑦 ∈ 𝑓(𝐼) from the given antecedents 𝑥 ∈ 𝐼.
Thus, the inverse 𝑓 −1 of the function 𝑓, gives the antecedents 𝑥 of the images 𝑦 by 𝑓.