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Inverse of f(x)=(x-3)/(x+2)

Inverse of f(x)=(x-3)/(x+2)-example-1
User Yuri Gor
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Answer:


f^(-1)(x)=(2x+3)/(1-x)

Explanation:

Find the inverse of the given function, f(x).


f(x)=(x-3)/(x+2)

(1) - Switch x and f(x)


f(x)=(x-3)/(x+2)\\\\\Longrightarrow x=(f(x)-3)/(f(x)+2)

(2) - Solve for f(x) using algebraic techniques


x=(f(x)-3)/(f(x)+2)\\ \\\\\Longrightarrow (f(x)+2)x=f(x)-3\\ \\\\\Longrightarrow xf(x)+2x=f(x)-3\\ \\\\\Longrightarrow 2x=f(x)-3-xf(x)\\ \\ \\\Longrightarrow 2x+3=f(x)-xf(x) \\\\\\\Longrightarrow 2x+3=f(x)(1-x)\\ \\\\\therefore f(x)=(2x+3)/(1-x)

(3) - Replace f(x) with f^-1(x)


f(x)=(2x+3)/(1-x) \\\\\Longrightarrow \boxed{\boxed{f^(-1)(x)=(2x+3)/(1-x) }}

Therefore, the inverse is found.

User Pivert
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