Answer and Explanation
First, we can convert f(x) to slope intercept form:
[tex]f(x) = \dfrac{x-4}{3}[/tex]
[tex]f(x) = \dfrac{1}{3}x - \dfrac{4}{3}[/tex]
Now, we can see that f(x) is a line with slope 1/3 and y-intercept at -4/3.
We can see that the green line has a y-intercept at -1 1/3, which is equal to -4/3, so f(x) is the green line.
This means that f⁻¹(x) is the blue line because inverse functions are reflections of the original over the line y = x (which is the red line).
We can identify the following information about f⁻¹(x):
- slope = 3
- y-intercept = 4 (it looks like the line is slightly misgraphed)
So, the function is:
f⁻¹(x) = 3x + 4
