Inverse functions are only defined if the original function is a one to one function, which means that every point on the x axis only corresponds to one point on the y axis. In fact we have already seen an inverse function in our exponential and log functions.
The inverse function can be found by switching around x and y (f(x)).
Take logs of both sides
Here is the graph of the two functions:
The inverse is a reflection of the original function in the black line y=x.
When the function is flipped to the inverse function the new domain becomes the old range and the old domain becomes the new range.
2014 exam 2
We know that there can only be an inverse function if the function is a one to one function.
If a cubic function has a point of inflection then it will be a one to one function, therefore our first step is to find the derivative.
Now we solve for x in f'(x)=0.
Therefore we have two turning points and it is not a one to one function, so we need to restrict the domein.
There are three sections of the graph where it is a one to one function
Only one of those are the same as the above which is the D:(∞–, -3) which is A in the multiple choice.
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