# A function is defined by f(x) = 6 / (2x+3) for x ≥ 0. Find an expression of the inverse in terms of x, and find its domain.

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justaguide | Certified Educator

The function `f(x) = 6 / (2x+3)` . A function f(x) and its inverse `f^-1(x)` are related by `f(f^-1(x)) = x`

For the given function `f(f^-1(x)) = x`

=> `6/(2*f^-1(x) + 3) = x`

=> `(2*f^-1(x) + 3) = 6/x`

=> `2*f^-1(x) = 6/x - 3`

=> `f^-1(x) = 3/x - 3/2`

The inverse function is `f^-1(x) = 3/x - 3/2`

The function f(x) is defined only for `x >= 0` , the domain of the inverse is x > 0.

**The domain of the inverse is **`{0, oo}`