Question

Question is attached​

Answer 1

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)`