Let R ={(x,y):y = 3x+3/x+1},then which of the following is equal to inverse? ?

To find the inverse of the relation R, we need to switch the x and y values and solve for y.

So, if we switch x and y in the relation y = 3x + 3/x + 1, we get x = 3y + 3/y + 1.

Now, we need to solve for y in terms of x:

x = 3y + 3/y + 1
x(y + 1) = 3y + 3
xy + x = 3y + 3
xy - 3y = 3 - x
y(x - 3) = 3 - x
y = (3 - x)/(x - 3)

Therefore, the inverse of the relation R is {(x, (3 - x)/(x - 3))}.

The inverse of a relation R is a relation R^-1 such that for all (x,y) in R, (y,x) is in R^-1.

In other words, the inverse of a relation is obtained by interchanging the domain and range of the relation.

The domain of the relation R is {x:y = 3x + 3/x - 1} and the range is {y:y = 3x + 3/x - 1}.

To find the inverse of R, we interchange the domain and range:

The domain of R^-1 is {y:y = 3x + 3/x - 1} and the range is {x:x = 3y + 3/y - 1}.

Simplifying the range of R^-1, we get:

x = 3y + 3/y - 1
x - 3y = 3/y - 1
x - 3y = 3 - y
x = 3 - y

Therefore, the inverse of the relation R is:

R^-1 = {(x,y):x = 3 - y}

Hence, the answer is (x,y):x = 3 - y.