find the inverse of y=(2x+1)/(y+3) , (x is not equal to 3) and solve inverse for y?

Answer 1

y=(2x+1)/(x+3), assuming this is the original function
Switch x and y,
x=(2y+1)/(y+3)
xy+3x = 2y+1
Solve for y,
y = (3x-1)/(2-x)
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Reason: y should be an explicit function here. Otherwise, it doesn't make sense to find its inverse because an implicit function contains both.

Answer 2

Switch the x's and y's and solve for y:

x = (2y + 1) / (x + 3)
x (x + 3) = 2y + 1
x^2 + 3x - 1 = 2y
(x^2 + 3x - 1) / 2 = y

So the inverse is (x^2 + 3x - 1) / 2

Answer 3

y=(2x+1)/(y+3)
y/(y+3) = 2x+1
[y(y+3) -1]/2 = x