 In this video, we provide the solution to question 21 for the practice final exam for math 1050 We're given the function f of x equals 4x minus 2 over 3x plus 1 Which is a one-to-one function by the way and we have to compute its inverse function So starting off with f of x here We're going to actually use the variable y here because the inverse function switches the roles of x and y So I want to be very explicit on whose x and whose y so this gives us y This is the equation that produces the graph of f to get f inverse Right, we swap the x and y around so we get x equals 4 y minus 2 over 3 y plus 1 We now want to solve for y so times both sides of the equation by 3 y plus 1 3 y plus 1 that way it cancels out on the left on the right hand side giving us x times 3 y plus 1 I actually want to distribute this so we end up with 3 x y plus x This on the right hand side would then be equal to 4 y minus 2 We then want to solve for the y here. We want to combine the y's so move the 4 y to the left hand side Move the non y the x to the other side, so we get 3 x y Minus 4 y notice here. That's the left hand side it since everything's divisible by y you can actually factor out the y Giving you 3 x minus 4. This is going to equal the right hand side, which is a negative x minus 2 So then divide both sides by the 3 x minus 4 3 x minus 4 and then this would then give us y equals Well, this is actually f inverse now label specifically who FM inverse is don't leave it up to guessing You're gonna end up with negative x minus 2 over 3 x minus 4 Like so and this is then the inverse function that we've just calculated