On the attached diagram you can see all graphs of functions b(x), d(x), m(x) and p(x).
Finding the inverse of a function f(x):
1. First, replace f(x) with y. This is done to make the rest of the process easier.
2. Replace every x with a y and replace every y with an x.
3. Solve the equation from Step 2 for y. This is the step where mistakes are most often made so be careful with this step.
4. Replace y with \(f^{-1}(x).\) In other words, you’ve managed to find the inverse.
5. Remember: the domain of f is the range of \(f^{-1}\) and the range of f is the domain of \(f^{-1}\).
Using this algorithm, you can find the inverse only in case C:
for m(x)=-7x:
1. y=-7x.
2. x=-7y.
3. y=-x/7.
4. \(m^{-1}(x)=-\dfrac{x}{7}\).
5. The domain and the range of m(x) are all real numbers as well as the domain and the range of \(m^{-1}(x).\)
Functions b(x) and p(x) are not one-to-one functions (see attached diagram), then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.
