The graph of f(x) is shown below. If f(x) and its inverse function, f^-1 (x), are both plotted on the same coordinate plane, where is their point of intersection?

Question

asked Jun 22, 2021 77.6k views

2 Answers

Joethemow · Answer 1 · 2021-06-28T10:40:58+0000

Answer:

(2,2)

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

$y-6=(0-6)/(3-0)(x-0)\\ \\y-6=-2x\\ \\y=-2x+6$

2. Find the equation of the inverse function
f^(-1)(x):

$y=-2x+6\\ \\y-6=-2x\\ \\x=-(1)/(2)(y-6)\\ \\x=-(1)/(2)y+3$

Change x into y and y into x:

y=-(1)/(2)x+3

3. Find the point of intersection solving the system of two equations:

$\left\{\begin{array}{l}y=-2x+6\\ \\y=-(1)/(2)x+3\end{array}\right.$

Equate right parts:

$-2x+6=-(1)/(2)x+3\\ \\-4x+12=-x+6\\ \\-4x+x=6-12\\ \\-3x=-6\\ \\x=2\\ \\y=-2\cdot 2+6=2$

Hence, the point of intersection has coordinates (2,2)