SOLUTION: How to solve for the inverse of: 1/ (2x) +3 ( three being beside the fraction not in the denominator

Question 1203645: How to solve for the inverse of: 1/ (2x) +3 ( three being beside the fraction not in the denominator

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

if you have

....swap variables

....solve for

so, inverse is

'=

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The response from the other tutor shows a standard formal method for finding the inverse of a function.

For many functions for which an inverse exists, another method which is often faster is to use the idea that an inverse function "gets you back where you started from".

The given function does the following to the input x to get the function value:
(1) multiply by 2 [x --> 2x]
(2) take the reciprocal [2x --> 1/(2x)]
(3) add 3 [1/(2x) --> 1/(2x)+3]

The inverse must perform the inverse operations in the reverse order:
(1) subtract 3 [x --> x-3]
(2) take the reciprocal [x-3 --> 1/(x-3)]
(3) divide by 2 [1/(x-3) --> 1/(2(x-3))]

ANSWER: The inverse function is

f^(-1)(x) = 1/(2(x-3))

RELATED QUESTIONS
Hi, I have to solve the following equation: 3/x+ 5/x+2 = 2 ^ Ive had... (answered by solver91311,josmiceli)
The denominator of a certain fraction is three times the numerator. If 2 is added to the... (answered by unlockmath)
This problem is throwing me off because of the negative exponent. If you are able to... (answered by jsmallt9)
solve 6/(x^2-9)- 1/(x-3) = 1 the 6 is the numerator and (x^2-9) is the... (answered by jim_thompson5910)
Solve the equation To clarify on the 1/3^x the denominator has the exponent not the... (answered by Alan3354)
I need help. I am trying to solve addition and subtraction of rational numbers problem. I (answered by ankor@dixie-net.com)
this fraction is read 3 and one-half minus 1 it is in quotation marks and then the... (answered by checkley71)
Hello, I am not sure how to solve this equation for x, since x is in the denominator. (answered by stanbon,MathLover1)
Solve 1/3x2-1/2x=1/6. The 2 beside the 1/3x is supposed to represent... (answered by ankor@dixie-net.com)