Question

Graph the inverse of the function.

Answer 1

Answer:

The graph of the inverse function is the same that the graph of the original function

Step-by-step explanation:

step 1

Find the equation of the function in the graph

Let

f(x) ---> the function in the graph

we know that

Is a linear function

take the points (0,6) and (6,0)

Find the slope of the linear function

$m=(0-6)/(6-0)\\m=-1$

Find the the equation of the linear function in slope intercept form

$f(x)=mx+b$

we have

$m=-1$

$b=6$ ---> the y-intercept is given

substitute

$f(x)=-x+6$

step 2

Find the inverse of the function f(x)

Let

y=f(x)

$y=-x+6$

Exchange the variables (x for y and y for x)

$x=-y+6$

Isolate the variable y

$y=-x+6$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=-x+6$

$f^{-1}(x)=f(x)$

In this problem the graph of the inverse function is the same that the graph of the original function