Answer:
(2,2)
Step-by-step explanation:
step 1
Find the equation of f(x)
is a line that passes through the points (0,6) and (3,0)
Find the slope
[tex]m=(0-6)/(3-0)=-2[/tex]
The function f(x) in slope intercept form is equal to
[tex]f(x)=-2x+6[/tex]
step 2
Find the inverse
Let y=f(x)
[tex]y=-2x+6[/tex]
Exchange the variables x for y and y for x
[tex]x=-2y+6[/tex]
Isolate the variable y
[tex]2y=-x+6[/tex]
[tex]y=-0.5x+3[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=-0.5x+3[/tex]
step 3
Solve the system of equations
[tex]f(x)=-2x+6[/tex]
[tex]f^{-1}(x)=-0.5x+3[/tex]
equate both functions
[tex]-0.5x+3=-2x+6[/tex]
solve for x
[tex]2x-0.5x=6-3[/tex]
[tex]1.5x=3[/tex]
[tex]x=2[/tex]
substitute the value of x in any of the functions
[tex]f(x)=-2(2)+6=2[/tex]
The solution is the point (2,2)
therefore
Their point of intersection is (2,2)
