help.. inverse?

Question

please help me to find the inverse of this and check by composition of function.

f(x) = x-4/x

please show me the solution.. thank you all!

a

Answer 1

Do you mean f(x) = (x-4)/x or f(x) = x - 4/x?
I'll assume it's the first one.

Replace f(x) with y.
y = (x-4)/x

Switch x and y
x = (y-4)/y

Solve for y
Start by multiplying both sides by y.
xy = y - 4
Subtract y from each side
xy - y = -4
Factor out y
y(x-1) = -4
Divide both sides by (x-1)
y = -4/(x-1)
This is your inverse.

To check you have to do two compositions: f(f^-1(x)) = x and f^-1(f(x)) = x.

I'll show you how to do one, and the other is similar.
f(f^-1(x))
= f(-4/(x-1))
= (-4/(x-1) - 4) / [-4/(x-1)]
Multiply the top and bottom by (x-1)
= (-4 -4(x-1)) / (-4)
= (-4 - 4x + 4) / (-4)
= -4x/-4
= x

Answer 2

f(x) = x-4/x Given
y = x-4/x f(x) = y
y = x/x - 4/x Equivalent to the former
equation.
y-1 = -4/x x/x = 1; 1 subtracted both sides
x(y-1) = -4 Multiply by x.
x = -4/y-1 = 4/1-y. Divide by (y-1).
Then interchange x and y. You may also multiply the inverse by -1/-1 to obtain a positive answer. This does not alter the equation because it is equivalent to multiplying by 1.

Answer 3

The problem is not well posed. A function f has an inverse if and only if f is one-to-one. This function is not one-to-one. For example, f(4) = 3 = f(-1) and f(2) = 0 = f(-2). UNLESS THE DOMAIN IS SUITABLY RESTRICTED, THE QUESTION MAKES NO SENSE.

Answer 4

y= x-4/x then = yx = x^2 - 4then x^2-yx -4 =0

x=[y±√(y² +16)] /2 for check if x=1 then y =-3 then we will use + sign then
x=[y+√(y² +16)] /2