A function f(x) and its inverse `f^-1(x)` are related by `f(f^-1(x)) = x`
For `f(x) = (3 -x)/2`
`f(f^-1(x)) = x`
=> `(3 - f^-1(x))/2 = x`
=> `3 - f^-1(x) = 2x`
=> `f^-1(x) = 3 - 2x`
The inverse function for `f(x) = (3 -x)/2` is `f^-1(x) = 3 - 2x`
To find the inverse of the function, interchange the variables and solve for ` y` .
`x = 1/2(3-y)`
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
`1/2(3-y) = x`
Multiply `x` by each term inside the parentheses.
Remove the parentheses around the expression `3-y` .
Move all terms not containing `y` to the right-hand side of the equation.
Divide each term in the equation by `-1` .
Find the composition `f(f^(-1)(x))`
Since `f(f^(-1)(x)) =x , f^(-1) (x) = 3- 2x` is the inverse of `f(x) = ((3-x))/2` .
Thus, the inverse of the given equation is
`f^(-1) (x) = 3 - 2x`