find the inverse
((3x)/(x-4))=y
this is as far as i got
(3y)/y-4=x
3y=xy-4x
Calculating the inverse of a function is easy.Just make x the subject of the equation, and replace y with x in the resulting expression
3y/(y-4)=x
3y=x(y-4)
3y=xy-4x
3y-xy= -4x
y(3-x)= -4x Divide with (3-x)
y= -4x/(3-x)= -4x/-(x-3)= 4x/(x-3)
4x/(x-3)
Is inverse function of 3x/(x-4)
To find the inverse of the given function, we need to swap the roles of x and y and solve for y.
Step 1: Start with the original equation:
((3x) / (x-4)) = y
Step 2: Swap x and y:
((3y) / (y-4)) = x
Step 3: Solve for y:
Multiply both sides of the equation by (y-4):
3y = x(y-4)
Distribute on the right side:
3y = xy - 4x
Rearrange the terms to group the y terms on the left side:
3y - xy = -4x
Factor out y:
y(3 - x) = -4x
Divide both sides by (3 - x):
y = (-4x) / (3 - x)
Therefore, the inverse of the function ((3x) / (x-4)) is y = (-4x) / (3 - x).