Inverse of a Functions please help?

Question

Here its given f(x) = 2/x+3 and its inverse it 2-3x/x .

How is that possible can u explain clearly and give examples !

like if f(x) = 3x/x+2 its f(x) inverse is -2x/x-3 , how is it ?

Answer 1

y = f(x) = 2/(x+3)

the inverse of y is (x+3)/2
but the inverse function means something else x = g(y) such that
g(f(x)) = x

(x+3)y = 2
x+3 = 2/y
x = -3 +2/y is the inverse function x = g(y)

check g(f(x)) = -3 +2/y = -3 + 2(x+3)/2 = x as required

Answer 2

hey ,
as y is the function F(x)=y= 2/x+3 ,

change places of y and x it will be


x = 2/(y + 3) ---> ( y + 3 ) = 2/x -----> make y in one side of
the equation -----> y = (2/x) - 3 ----> y = ( 2 - 3x ) / x

finally F(x) = ( 2 - 3x ) / x the invers.

i'll give a simple example by me ,

f(x) = x + 1 find the inverse ,

1) y = x +1
2) change x and y x = y + 1
3) now y must be n one side alone , adding -1 , so x - 1 = y
4) F(x) = x - 1 the inverse
,,,,,
by the way , if u have more than one x when changing them by Y change alllll of the Xes
try to solve this one , f(x) = (x+3) / (x-4)

the answer is , F(x) = ( 3+4x ) / ( x - 1 ) the inverse

hope u got it , and good luck :)

Answer 3

f(x) = 2 / (x+3)
now you are looking for an inverse function g such that : f ( g(x) ) = x
because that is the meaning of g being the inverse of f.

So fill in the stuff and play :

f(g(x)) = 2 / (g(x)+3) = x

2 / (g(x)+3) = x
=>
1/(g(x) + 3) = x/2
=>
g(x) + 3 = 2/x
=>
g(x) = (2/x) - 3.

let us see if it is correct :
take a number say x = -1
then f(-1) = 2 / (-1 + 2) = 1
and g(1) = 2/1 - 3 = -2 yess!

Answer 4

If you're given that a function is an inverse of another, it follows that if one function is f(x) and the other is g(x),

f(g(x)) = g(f(x)) = x.

Let's verify that.

Let f(x) = 2/(x + 3) and g(x) = (2 - 3x)/x

Then

f(g(x)) = f [ (2 - 3x)/x ] = 2/[ (2 - 3x)/x + 3 ]
= 2x/(2 - 3x + 3x)
= 2x/2
= x

and you can obtain similar steps for g(f(x)).

Answer 5

Take the term f(x) and change it to , say, y

Then work the equation around, so you get x = something

then change the y's into x's

ex: f(x) = 2/(x+3)

y = 2/(x+3)

(x+3)*y = 2

x + 3 = 2/y

x = 2/y - 3

x = 2/y -3y/y

x = (2-3y)/y

so, you have f(x)^-1 = (2-3x)/x

Answer 6

y= 3x/(x+2)
First, solve for x:
y(x+2) = 3x
yx +2y =3x
2y = 3x-yx
2y = x(3-y)
2y/(3-y) = x
Now interchange x and y getting:
2x/(3-x) =y=f^-1(x) which is same as -2x/(x-3)

Answer 7

There is a formula to find the inverse of a linear function.
If f(x)= ax+b
and its inverse will be f^(-1)(x) = (1/a)x+(-b/a)

Answer 8

let y = f(x)
then x = f^-1(y)

now y = 2/(x+3)

let us try to write x as a function of y that if f^-(y)

y(x+3) = 2
or yx +3y = 2
or x = (2-3y)/y
f^-(y) = (2-3y)/y
put x for y
f^-(x) = (2-3x)/x

Answer 9

just swap f(x) with x, and rearrange to get f(x) on its own again

f(x) = 3x/(x + 2)
=> x = 3f(x)/(f(x) + 2)
=> x(f(x) + 2) = 3f(x)
=> xf(x) - 3f(x) = -2x
=> (x - 3)f(x) = -2x
=> f(x) = -2x/(x - 3)