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Question is attached​-example-1
User Lucapette
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Hello!


\large\boxed{f^(-1) = (5x+2)/(4x-2), f^(-1)(3) = (17)/(10) }


f(x) = (2x +2)/(4x - 5)

Find the inverse by swapping the x and y variables:


y = (2x +2)/(4x - 5)\\\\x = (2y +2)/(4y - 5)

Begin simplifying. Multiply both sides by 4y - 5:


x(4y - 5) = 2y + 2

Start isolating for y by subtracting 2 from both sides:


x(4y - 5) -2 = 2y

Distribute x:


4yx - 5x - 2 = 2y

Move the term involving y (4yx) over to the other side:


- 5x - 2 = 2y - 4yx\\\\

Factor out y and divide:


- 5x - 2 = y(2 - 4x)\\\\y = (-5x-2)/(-4x+2) \\\\y = (-(5x + 2))/(-(4x - 2)) \\\\y^(-1) = (5x + 2)/(4x - 2)

Use this equation to evaluate
f^(-1)(3)


f^(-1)(3) = (5(3) + 2)/(4(3) - 2) = (17)/(10)

User Hafizul Amri
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