Need help on this inverse function question

[Iwant2learn]

Given the function, f(x) = 24/(1)X+2 , X does not equal to -2/1

find the value of k if f^-1(k) = k


I had calculated the inverse function for f(x) = 24/(1)X+2 which is f^-1(x) = 24-2x/x,
I had tried to substitute x with k but still got the wrong answer.

any helps would be kindly appreciated

 

[Deleted member 4993]

Given the function, f(x) = 24/(1)X+2 , X does not equal to -2/1

find the value of k if f^-1(k) = k


I had calculated the inverse function for f(x) = 24/(1)X+2 which is f^-1(x) = 24-2x/x,
I had tried to substitute x with k but still got the wrong answer.

any helps would be kindly appreciated

You have to write the function properly for us to help you

You wrote

f(x) = 24/(1)X+2 \(\displaystyle \to\ \ \) that means \(\displaystyle \to\ \ \) f(x) = 24/(1)X+2 = 24 * X + 2

I am assuming that you did not intend to write that. Also note that on the left-hand-side you wrote f(x) but on the right-hand-side you have (capital) X, you did not have any small x. Please be consistent. Please insert grouping symbols with () to indicate order of operation.

I did not understand the use of (1) in f(x) = 24/(1)X+2

Please review the definition and the method of inverting a function in your textbook. You can get a quick/easy overview at:

Finding the Inverse of a Function - Purplemath...........
www.purplemath.com › modules › invrsfcn3

Please come back with "corrected" problem statement and also

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[HallsofIvy]

I am going to assume you mean f(x)= 24/(x+ 2). To find a value of k such that f^{-1}(k)= k. You don't really need to find the inverse function because, taking f of both sides, that equation is equivalent to f(k)= 24/(k+2)= k. So 24= k(k+2)= k^2+ 2k.

But, yes, if f(x)= 24/(x+ 2) then x+ 2= 24/f(x), x= 24/f(x)- 2 so f^(-1)(x)= 24/x- 2 which is the same thing as f^(-1)(x)= (24- 2x)/x (the parentheses are important!). f^(-1)(k)= (24- 2k)/k= k when 24- 2k= k^2, 24= k^2+ 2k as before.