If h(x)=3/(2x+1), find h^-1(x)

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To find the inverse of a function, h^(-1)(x), we need to switch the roles of x and y. In other words, we need to solve for x in terms of y.

To find h^(-1)(x), let's start by rewriting h(x) with y in place of h(x):
y = 3/(2x + 1)

Now, let's solve this equation for x in terms of y.
First, let's multiply both sides of the equation by (2x + 1) to eliminate the denominator:
y(2x + 1) = 3

Expanding the left side, we get:
2xy + y = 3

Next, let's isolate the term with x on one side:
2xy = 3 - y

Finally, let's divide both sides of the equation by 2y to solve for x:
x = (3 - y) / (2y)

This gives us the inverse of the function h(x):
h^(-1)(x) = (3 - x) / (2x)