fx 3x 67x 8 Show that f is onetoone Find an explicit expr

f(x) = 3x + 6/7x - 8 Show that f is one-to-one. Find an explicit expression for f^-1. State the domain and range of f. If your expression for f^-1 were correct, what should you expect to get if you simplify f(f^-1(x))? Evaluate (f f^-1)(x). You do not need to simplify this expression.

Solution

x = (-8y - 6)/(-7y + 3)

Then inverse of f(x) = (-8x - 6)/(-7x + 3)

Range = Not solvable

                            = (24x + 18 + 42x -18)/(56x + 42 – 56x + 24)

                             = 66x/66 = x