a) The function is not defined when the denominator is 0, find the values of x for which the denominator is not zero. That is the domain.
Consider what happens to the value of the function when x tends toward the limits in the domain (Hint the range is (0,1/2) )
b) If f is not one-to-one then there are two different values a and b such that f(a)=f(b)
Put a and b into your equation and either prove that f(a) can't equal f(b) or find the values of a and b so that f(a)=f(b)
c) Solve your equation so that you have x on its own equal to a function of y, then switch the places of the x's and y's to find the inverse function as a function of x
d) The inverse function involves a log. Remember that for $\displaystyle log(\frac{m}{n}) $ to be defined $\displaystyle \frac{m}{n}$ must be greater than zero and n cannot equal zero.
Note to anyone else posting advice, you might have been taught a 'one-to-one' function as an 'injective' function.