Share
Explore BrainMass

# Exponential Functions and their Inverse and Graphs

1. One example of an exponential function is f(x) = 4x. Its inverse can be found this way:
y = 4x
x = 4y
x = log4y
y = log4x
An example of points to plot to create the graphs are given:

F(x) F1(x)
(1, 4) (4, 1)
(0, 1) (1, 0)
(2, 16) (16, 2)
(-1, .25) (.25, -1)

3. For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
include the reasons for graphically representing the effect in a particular way. scan the graph you've plotted and post it along with your response.

X Ex E2x
0 1 1
1 2.72 7.39
2 7.39 54.6
3 20.09 303.43
4 54.6 2980.96

X Log(x) Log(2x)
0 Undefined Undefined
1 0 .3
2 .3 .6
10 1 1.3
20 1.3 1.6
With the first set, the graph rises twice as fast when doubled, making it much steeper. However, with the second set, when x is doubled it only raises the graph by .3. This is because log (a*b) = log (a) + log(b). Since log(2)=.3 (or 100.3 = 2), the graph is raised by this constant regardless of the value of x)

#### Solution Preview

Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.
===============================================================================

1. One example of an exponential function is f(x) = 4^x. Its ...

#### Solution Summary

This solution deals with exponential functions. I have shown what happens to the graph of some exponential functions when the argument of the function is doubled. Solution also includes three graphs.

\$2.19