Having simplified e(f(x)), we see that it equals x. Therefore, the value of e(f(-4)) must be -4.
e(f( -4))= -4
c
If we draw both graphs on the same set of axes, they will be reflections of each other in y=x. This is true for all functions and their inverse.
d
The domain and range shows the x- and y-values that a graph can take on. Let's identify these intervals for f(x). We will also mark a few points on the graph which will be useful when we draw the inverse.
The graph goes from -5 and to the right on the x-axis. It also goes from 1 and up on the y-axis. With this information, we can identify the range and domain of f(x).
Domain f(x): & x≥ -5
Range: f(x): & y≥ 1
Any point on the graph of the function has a corresponding point on its inverse where the x- and y-values are swapped. Since we have identified a few points on f(x), we can identify the corresponding points on the inverse.
|c|c|
[-1em]
f(x) & e(x) [0.2em]
[-1em]
(-5,1) & (1,-5) [0.2em]
[-1em]
(-4,2) & (2,-4) [0.2em]
[-1em]
(4,4) & (4,4) [0.2em]
The graph of the inverse can now be drawn by connecting the points on e(x). We will also mark the domain and range as we did with f(x).
Just like the inverse swaps the x- and y-coordinates of all points on the function, it also switches the domain and range. We can see this in the diagram as well.
Domain e(x):& x≥ 1
Range e(x):& y ≥ -5
