What is the inverse of f(x) = (3 - x)/2

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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`

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kingattaskus12 | (Level 3) Adjunct Educator

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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.

`(3-y)=2x `


Remove the parentheses around the expression `3-y` .

`3-y=2x `


Move all terms not containing `y` to the right-hand side of the equation.

`-y=2x-3 `


Divide each term in the equation by `-1` .

`y=3-2x `


Find the composition `f(f^(-1)(x))`  

`f(3-2x)=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`  

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