Answer:
(2,2)
Step-by-step explanation:
1. Find the equation of the function f(x). The graph of this function passes through the points (3,0) and (0,6). Then its equation is
[tex]y-6=\dfrac{0-6}{3-0}(x-0)\\ \\y-6=-2x\\ \\y=-2x+6[/tex]
2. Find the equation of the inverse function [tex]f^{-1}(x):[/tex]
[tex]y=-2x+6\\ \\y-6=-2x\\ \\x=-\dfrac{1}{2}(y-6)\\ \\x=-\dfrac{1}{2}y+3[/tex]
Change x into y and y into x:
[tex]y=-\dfrac{1}{2}x+3[/tex]
3. Find the point of intersection solving the system of two equations:
[tex]\left\{\begin{array}{l}y=-2x+6\\ \\y=-\dfrac{1}{2}x+3\end{array}\right.[/tex]
Equate right parts:
[tex]-2x+6=-\dfrac{1}{2}x+3\\ \\-4x+12=-x+6\\ \\-4x+x=6-12\\ \\-3x=-6\\ \\x=2\\ \\y=-2\cdot 2+6=2[/tex]
Hence, the point of intersection has coordinates (2,2)
