Answer :

The

function

given is f(x) = x/(x + 3) is defined from the set A to the set B. The

inverse

of the given function is f^-1(x) = 3x / (1 - x).

To find its inverse we will first find the

range

of the given function f(x). We know that the range of f(x) can be found by applying values to the function from the domain A. Range of f(x) : Let y = f(x) => y = x/(x+3) => y(x+3) = x => xy + 3y = x => x = 3y / (1-y). So, the range of the function f(x) is {y|y < 1} and x = 3y / (1-y). where y<1. Now, let us consider the inverse of the function. The inverse of the function can be defined as follows: f^-1(x) => f(x) = y => x = f^-1(y). Now, substitute the value of f(x) from the function in the equation above: x = f^-1(y) => x = y/(y+3) => y = 3x / (1 - x). Hence, the inverse of the function is f^-1(x) = 3x / (1 - x). The given function is f(x) = x/(x + 3) and it is defined from the

set

A to the set B. To find its inverse, first we need to find the range of the given function f(x). We know that the range of f(x) can be found by applying values to the function from the

domain

A. By solving this we can get the range of the function as {y|y < 1} and x = 3y / (1-y) where y<1. The inverse of the function can be defined as follows: f^-1(x) => f(x) = y => x = f^-1(y). Substitute the value of f(x) from the function in the equation above. This gives x = y/(y+3) => y = 3x / (1 - x). Therefore, the inverse of the function is f^-1(x) = 3x / (1 - x). Hence, we found the inverse of the given function.

Therefore, the inverse of the given function is f^-1(x) = 3x / (1 - x).

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