SOLUTION: Hi all, Im having trouble with the following Function and Domain problem(s).
The function f is defined by y = f(x) = 2 ln 4x, 0:01 <= x >= 1 .
(a) Solve for x in terms of y, and
Algebra.Com
Question 209169: Hi all, Im having trouble with the following Function and Domain problem(s).
The function f is defined by y = f(x) = 2 ln 4x, 0:01 <= x >= 1 .
(a) Solve for x in terms of y, and hence and the formula for the inverse
function f^(-1)(x).
b) Write down the domain of f^(-1)
Any help would be most appreciated.
-Nick.
Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The function f is defined by y = f(x) = 2 ln 4x, 0:01 <= x >= 1 .
(a) Solve for x in terms of y, and hence and the formula for the inverse
function f^(-1)(x).
---------------------------
y = 2*ln(4x)
ln(4x) = y/2
4x = e^(y/2)
x = (1/4)e^(y/2)
Interchange x and y to get the equation of the inverse.
y = (1/4)e^(x/2)
---
Do
b) Write down the domain of f^(-1)
Since the Range of y = 2*ln(4x) is f(0.01)
which is -6.438 < y < 2.7726
the Domain of f^-1(x) is -6.438 < x <= 2.7726
==================================================
Cheers,
Stan H.
Reply to stanbon@comcast.net or algebra.com
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Hi Nick!!
Given , you must solve for x by "undoing" all the operations that were done to it. You must undo mult by 2, undo the "ln" function, and undo multiplication by 4. That brings you down to x.
Start by dividing both sides by 2:
In order to "undo" the "ln", you must raise both sides as a power of e:
Last, divide both sides by 4:
In the above statements, y represents f(x).
NOW, if you interchange the x and the y, the NEW y represents the inverse function .
R^2
Dr. Robert J. Rapalje, Retired
Seminole Community College
Florida
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