Let f(x)= x / x-4. Find F-1 (Inverse)?

Question

That's supposed to be F with a superscript of -1 not like an exponent or anything

Answer 1

y = x / (x-4)

Switch x and y and solve for y:

x = y / (y-4)

Multiply both sides by y-4

x(y-4) = y

xy - 4x = y

xy -y = 4x

y(x-1) = 4x

y = 4x / (x-1)

or

f(-1) = 4x / (x-1)

Have a good day!

Answer 2

y = x/ (x-4)

switch y and x: x = y / (y-4)

solve for y, it will be f inverse

x/1 = y/ (y-4)

cross multiply: 1y = x(y-4) = xy - 4x

move the xy over: y - xy = -4x

factor out y: y(1 - x) = -4x

divide by (1-x): y = F-1 = -4x/(1-x) or 4x / (x - 1)

Answer 3

Let y = x / (x - 4), then solve for y.  You get x = 4y / (y - 1) which is the inverse function.  To check, plug in the expression for y and see if you get x = x.

Answer 4

You should really use parenthesis, it makes it a lot easier to understand.

f(x)=x/(x-4)----->just rewrite by replacing f(x) with y

y=x/(x-4)------>now, switch x and y

x=y/(y-4)---->this is the inverse function, but we must solve for y

x=y/(y-4)----->multiply by (y-4)

x(y-4)=y------>just open it up

xy-4x=y----->bring everything that has y to the same side, add 4x

xy=y+4x---->subtract y

xy-y=4x----->factor out the y term

y(x-1)=4x---->divide by (x-1)

y=4x/(x-1)--->replace y with f(x)

f(x)=4x/(x-1)---->inverse function

Hope this helped. Peace