h(x)= 2x/(1-x) find h^-1(x)?

Answer 1

No, Band84 isn't right. I think that in this case the index -1 means the inverse function.

One way of doing this is to write the function as

y = 2x/(1-x),

then get the inverse by swapping x and y:

x = 2y/(1-y)

and then make y the subject of this equation.

You should get

y = x/(2+x)

and so
(h^-1)(x) = x/(2+x)

I see a couple of other people submitted this solution while I was typing it out. Another way of doing it is this:

The expression can be written as
(2(x-1) + 2)/(1-x)
= -2 + 2/(1-x)

In words this can be stated as
Start with x
Multiply by -1
Add 1 [At this stage we have 1-x]
Invert
Multiply by 2
Subtract 2.

To find the inverse function, do the opposites of these operations in the reverse order, thus:

Add 2, giving x+2
Divide by 2, giving (x+2)/2
Invert, giving 2/(x+2)
Subtract 1, giving 2/(x+2) -1
Multiply by -1, giving 1 - 2/(x+2)

and of course this last expression simplifies to
x/(x+2)

Answer 2

h^-1(x)=x/(2+x)

Answer 3

Given h(x)=2x/(1-x)
let h^-1(x)=y
=> x=h(y)
=> x=2y/(1-y),making 'y' as subject, we get
y=x/(x+2)
therefore, h^-1(x)=x/(x+2)
NOTE: As one of the answers given,h^-1(x) is not equal to 1/h(x).

Answer 4

start up by way of removing the parentheses (distributive assets): 5x+12-4x-6-2x-5+2x=a million+1x combine like words (upload constants with different constants and multiples of the variable at the same time): (5x-4x-2x+2x)+(12-6-5)=a million+1x 1x+a million=a million+1x in case then you definitely resolve this for x, you will discover that the x words disappear: 0=0 this implies you may plug in any real value for x and function the equation be real.

Answer 5

h^-1 (x) = 1/h(x) = (1-x)/2x

Answer 6

to find the inverse of function try this

y=2x/(1-x)

and solve for x

(1-x)y=2x
y-xy=2x
y=2x+xy
y=x(2+y)
y/(2+y)=x

h(x)= x/(2+x)

Answer 7

y = 2x/(1-x)
y-xy = 2x
y = 2x+xy = x(y+2)
x = y/(y+2)
inv(h(x)) = x/(x+2)

Answer 8

h(x) = (2x)/(1 - x)

y = (2x)/(1 - x)
x = (2y)/(1 - y)
x - xy = 2y
-xy - 2y = -x
-(xy + 2y) = -x
xy + 2y = x
y(x + 2) = x
y = x/(x + 2)

ANS :

h^-1(x) = x/(x + 2)