MHB Finding the Inverse of f(x) = x/(x+4)

AI Thread Summary
To find the inverse of the function f(x) = x/(x+4), the first step is to replace f(x) with y, leading to the equation y = x/(x+4). Rearranging gives xy + 4y = x, which can be transformed into x(y - 1) = -4y. Solving for x results in x = -4y/(y - 1). This method clarifies the process of isolating x to determine the inverse function.
RidiculousName
Messages
28
Reaction score
0
Hello, I am trying to find the inverse of f(x) = x $$ \div$$ (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x $$\div$$ (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?
 
Mathematics news on Phys.org
RidiculousName said:
Hello, I am trying to find the inverse of f(x) = x $$ \div$$ (x+4)

IIRC i need to replace f(x) with y and solve for x.

I've tried to do y = x $$\div$$ (x+4) becomes y(x+4) = x then xy + 4y = x but I can't reduce the amount of x to one.

What am I doing wrong in this problem?

Hi Mr. Ridiculous, welcome to MHB! ;)

We can take it a couple of steps further:

xy + 4y = x
xy - x + 4y = 0
xy - x = -4y
x(y - 1) = -4y
x = -4y $$\div$$ (y-1)
 
Thanks! I forgot I could leave the right side of the equation as zero.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

I What are the applications of inverses of vector functions?
Replies
17
Views
3K
I Calculating the inverse of a function involving the error function
Replies
3
Views
2K
I Finding the inverse tangent of a complex number
Replies
2
Views
2K
B Inverse Functions: Why rewrite as y=f(x) ?
Replies
11
Views
2K
MHB Find Inverse of Rational Function
Replies
7
Views
2K
B Are Inverse Problems More Complex Than Direct Problems in Mathematics?
Replies
13
Views
3K
B Inverse Functions vs Inverse Relations
Replies
4
Views
3K
I My attempt to understand horizontal transformations of functions
Replies
6
Views
2K
MHB Solving Function Expressions h(x): (x+a)2 +b & h-1 Range
Replies
7
Views
1K
MHB What are the domain and range for the inverse function $f^{-1}$ of $f$?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top