The exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex
equals its own derivative. The exponential function is used to model
phenomena when a constant change in the independent variable gives the
same proportional change (increase or decrease) in the dependent
variable. (Source from Wikipedia).It is otherwise Written as exp(x).Here
we are going to see about preparation about inverse exponential
function and its example problems.
Preparation for finding the inverse of the function:
- First we got to to replace f(x) with y
- Switch x‘s y‘s
- Solve for y
- Replace y of f –(x)
Preparation problems for preparation for inverse exponential function:
pro1 : Find the inverse function of the following y = 3x+1
Sol : The given function is y = 3x +1
Following the above procdure to find the inverse of the function
First we have to Interchange x and y value
x=3y+1
Then now solve for y
Add both sides -1 then the equation will be
x-1 =3y + 1 -1
x-1=3y
Divide both sides 3 we get ,
y = `(x-1) / (3)`
Therefore the inverse function is (x-1) / (3)
Example for inverse of exponential function:
Pro 2: Find the inverse of the following exponential function,
y = 5. 6 (3x-4) +7
Sol : Interchange the x and y value then the equation will be,
x= 5. 6 (3y-4) +7
Now we solve for y
Add both sides -7 we get
x-7 = 5. 6 (3y-4) +7-7
x-7 = 5. 6 (3y-4)
Divide both sides 5 we get,
`(x-7) / (5)` = `(5. 6 (3y-4)) / (5)`
`(x-7) / (5)` = 6 (3y-4)
Take both sides log then the equation will be ,
Log 6 `((x-7) / (5))` = log 6 6 (3y-4)
Log 6 `((x-7) / (5))` = 3y-4
Add both sides +4
Log 6 `((x-7) / (5))` + 4 = 3y
Both sides divide 3 we get
`{Log 6 ((x-7) / (5) + (4))} / (3)` = `(3y) / (3)`
`{Log 6 ((x-7) / (5) + (4))} / (3)` = y
Therefore the inverse exponential function is `{Log 6 ((x-7) / (5) + (4))} / (3)` = y
Hence the preparation of inverse exponential function is explained,
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