Inverse Exponential Functions
Introduction for inverse exponential functions:
In mathematics, 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. The exponential function is often written as exp(x), especially when the input is an expression too complex to be written as an exponent.
The inverse exponential function is in the form of 1/ ex. Logarithmic functions are inverse of exponential functions.
Inverse Exponential Functions and Rules:
Inverse of exponential functions:
A function f may have the same value for difference numbers in its domain. Example, if f(x) = x^2, then f (2) = 4 and f (-2) = 4, but 2 -2. For the inverse of a function to be essential that different numbers in the domain always give different value of f.
General logarithm functions:
y = log a x , where a = base, a>0 and a and x = variable which takes values x >0. If the base of a logarithm function is not specified, Then the base of the function is considered to be 10.
Natural logarithmic functions:
f (x) = ln x is the natural exponential function,
f- -1(x) = ex
y = ex if and only if x = ln y
y = ln x, here base is e
Rules of Exponentiation:
The rules used in manipulate exponential functions are:
bx+y = (bx)(by)
bxy = (bx)y
b0 = 1
b -x = 1/(bx)
Other Rule:
Multiplication Rule: bn.bm = bn+m
Division Rule: bx / by = bx-y
Power Rule: b(x)y
Multiplicative Distribution :(ab)x = ax.bx
Quotient Distribution : (a/b)x = ax / bx
Example Problem for Inverse Exponential Functions:
Problem 1:
Convert to inverse exponential function:
8=2x
Solution:
log2 (8) = x
Problem 2:
Convert to inverse exponential function
5=3y
Solution:
log3 (5) = y
Problem 3:
Find the formula inverse of the function f(x) = (2x 5) / (3x + 4)
Solution:
To find the inverse function we follow the steps outlined in the tutorial. First, We write the formula for the function as y = f(x)
y = (2x 5) / (3x + 4)
We must solved this function for x in terms of y.
y (3x+4) = (2x 5)
3xy + 4y = (2x 5)
4y + 5 = 2x 3xy
4y + 5 = x( 2 3y )
4y + 5 / 2 -3y = x
x = (4y + 5) / (2 3y)
Now we simply interchange the variable x and y, so that the inverse function is in terms of y,
y = (4x + 5) / (2 3x)
Therefore the inverse of function f(x) = (2x 5) / (3x + 4) is given by the formula
f -1 = (4x + 5) / (2 3x)
by: Omkar Nayak
Shindaeyang Paper Co., Ltd. - Company Capsule How To Deactivate Facebook Account Or Delete It? Tips To Find A Certified Public Accountant The Must Know Superstition Beliefs Of Gemstones Choosing The Right Building Materials Company Get Started With Ibm 000-n18, 000-n19, 000-n23 Exam Get Best Deals On Branded Mobiles, Cameras @ Shopllers What Is A Cavity Mumbai Malls Usher In Diwali Festivities With Product Offerings From Taiwan Excellence Lifestyle! Ball Joint 5 Challenges In Kindergarten The Power Of Interactive Learning That Can Change The World How To Prepare Ibm 000-n24, 000-r09, 000-r12 Exam