How to find inverse function?

Question

How do you find the inverese function of f(x)=x/(x+1). Inverse means replacing x and y not reciprocal. I already know the answer (by pure luck) but I don't know how to figure it out. Please help me!

I know how to do inverses, but this one is crazy! It's not that easy.
The answer is f inverse of x= (-x)/(x-1)
How do I get to it?

Answer 1

f(x) = x/(x + 1)

To find the inverse, first, let y = f(x). Then

y = x/(x + 1)

Like you already know, swap the x and y terms.

x = y/(y + 1)

And now, solve for y. Multiply both sides by (y + 1),

x(y + 1) = y

Now, expand the left hand side.

xy + x = y

Bring everything with a y to the left hand side, and everything else to the right hand side.

xy - y = -x

Now, factor y out, on the left hand side.

y(x - 1) = -x

Divide both sides by (x - 1), to get

y = -x / (x - 1)

All that's missing is your concluding statement. Remember that you wanted to solve for f^(-1)(x), so that's what you say.
Therefore,

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

Answer 2

Many have answered, so I won't repeat what has been said. However, it is a good idea to check your solution if you are not comfortable with the process.

To check, select a number for x. If you chose x = 1, f(x) = 1/ 1+1 = 1/2. Therefore, in the inverse function, if I substiture the answer 1/2 in for x, I should get 1 as my y, or f^-1(x)

Answer 3

Step 1) put y in place of f(x)

Step 2) Switch the x's and y's (put an x where the y was, and put y's where the x's are

Step 3) Solve for y

Step 4) you have the inverse function

Answer 4

y=x for a inverse relation deliver you modify y<=> x ie reflect the function interior the line y=x outline the relation deliver f (g) = g(f) for strict inverse function you want to restriction the domains and levels of both relations contributors f & g such that f & g are purposes you may now outline the invertible function. seem up the definition of a function and also you may want to make certain that is somewhat trivial. degenerate case the x axis (function) invert, the y axis (no longer and by no ability a function) this can be generalized

Answer 5

I remember this one. This problem was invented by Archimedes and is called the "Are you a tricky little bugger" problem. The trick (after three pages of desperate scribbling) is this:
x/(x+1) = y
=> (xy + y)/x = 1
=> y + (y/x) = 1
=> y/x = 1 - y
=> y = x(1-y)
=> y/(1-y) = x

And switch x and y as normal. I see someone solved this an hour ago, but at least I have my dignity.

Answer 6

ok so you rewrite as f(x) = y = x/(x+1)

Now to get the inverse you switch y and x. You now get:

g(x) = inverse of f(x)
x = y/(y+1)
y = x*(y+1) = xy + x
y - xy = x
y*(1-x) = x

g(x) = y = x/(1-x)

Answer 7

let y=x/(x+1);
y(x+1)=x;
yx+y=x;
y=x-yx;
x(1-y)=y;
rearranging the equation for x in such a way--
x=y/(1-y);

and now replace 'x' with 'y'
i.e y=x/(1-y)...its Ur answer

Answer 8

you do not replace x and y, you have to solve for x - that is isolate x instead of y on one side of the equation.

Answer 9

1. replace f(x) with y
2. switch x and y in your equation
3. solve for y
4. rewrite y as f^-1(x)

ta-da!!!!

Answer 10

f(x)= x/(x+1)
x=y/(y+1)...
Don't remember the rest. Please post the answer and I might be able to finish