G (x) = 3x/x-5
2007-03-17 05:05:19 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
G(x) = 3x / (x - 5)
To find the inverse, let G(x) = y. Then
y = 3x / (x - 5)
Now, swap the x and y terms; for every y term that appears, put an x; for every x term, put a y.
x = 3y / (y - 5)
Now, solve for y. To do so, first multiply both sides by (y - 5).
x(y - 5) = 3y
Expand the left hand side.
xy - 5x = 3y
Move everything with a y term to the left hand side; everything goes to the right hand side.
xy - 3y = 5x
Factor y.
y(x - 3) = 5x
Divide both sides by (x - 3)
y = 5x / (x - 3)
Make your concluding remark by changing y to G^(-1)(x).
G^(-1)(x) = 5x / (x - 3)
2007-03-17 05:14:27 · answer #1 · answered by Puggy 7 · 0⤊ 0⤋
G(x) = 3x / x-5 => G-1(x) = 5x/x-3
2007-03-17 05:12:26 · answer #2 · answered by alwayss_ready 3 · 0⤊ 0⤋
inverse of function is very easy to do
let say
y=3x/x-5
y(x-5)=3x step: send x-5 on the left
xy-5y=3x
xy-3x=5y regroup all x
x(y-3)=5y
x=5y/y-3
therefore g inverse x = 5x/x-3
2007-03-17 05:15:24 · answer #3 · answered by Anonymous · 0⤊ 0⤋
x E {0 or 8}
2007-03-17 05:11:43 · answer #4 · answered by Cappy 2 · 0⤊ 0⤋
(x-5)/3x
because [(x-5)/3x] X [3x/(x-5)]=1
2007-03-17 05:10:38 · answer #5 · answered by gummstein 1 · 0⤊ 1⤋
y = 3x / x - 5
xy -5y = 3x
x(y - 3) = 5y
x = 5y / y - 3
Replace y by x
G^-1(x) = 5x / x - 3
This is the inverse function
2007-03-17 05:11:47 · answer #6 · answered by nayanmange 4 · 0⤊ 0⤋