inverse function

Question

how do I get the inverse function of f(x) = (-6x+7)/(5x-4)? with explanation please

Answer 1

y = (-6x + 7)/(5x -4)

switch the x and y and solve for the new y

x = (-6y+7)/(5y-4)

5xy -4x = -6y + 7

5xy+6y = 4x+7

y(5x+6) = 4x+7

y = (4x+7)/(5x+6)

f^-1(x) = (4x+7)/(5x+6) is the inverse function

you can check it by seeing if it reverses (x,y) or (x, f(x)) values to (y,x) for f^-1(x)