g(x) = 3x+5 / x-1
find the inverse function
thanks man
boo
scary
To find the inverse function of g(x), we need to swap the roles of x and y and solve for y.
Let's start by swapping x and y in the equation:
x = (3y + 5) / (y - 1)
Next, let's multiply both sides of the equation by (y - 1) to eliminate the fraction:
x(y - 1) = 3y + 5
Now distribute on the left side:
xy - x = 3y + 5
Let's gather the terms with y on one side and the constants on the other side:
xy - 3y = x + 5
Factor out y:
y(x - 3) = x + 5
Divide both sides of the equation by (x - 3) to solve for y:
y = (x + 5) / (x - 3)
Now we have solved for y. The inverse function of g(x) is f(x) = (x + 5) / (x - 3).
I will assume you meant
g(x) = (3x+5)/(x-1)
step 1: interchange the x and y variables
inverse is: x = (3y+5)/(y-1)
step 2: solve this new equation for y
cross-multiply
3y+5 = xy - x
3y - xy = -5-x
y(3-x) = -5-x
y = (-5-x)/(3-x)
or
y = (5+x)/(x-3)
so g^-1 (x) = (5+x)/(x-3)
check with x=2 (or any other value of x)
g(7) = 11/1 = 11
g^-1(11) = 16/8 = 2