Question

How do I graph the function and it's inverse

Answer 1

Answer:

The graph both functions in the attached figure

Step-by-step explanation:

we  have

$f(x)=-3x+3$

Find the inverse of f(x)

Let

$y=f(x)$

$y=-3x+3$

Exchange the variables x for y and y for x

$x=-3y+3$

Isolate the variable y

$3y=-x+3$

$y=-\frac{1}{3}x+1$

Let

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

$f^{-1}(x)=-\frac{1}{3}x+1$ -----> inverse function

To graph the functions find the intercepts

The y-intercept is the value of y when the value of x is equal to zero

The x-intercept is the value of x when the value of y is equal to zero

For $f(x)=-3x+3$

The y-intercept is the point $(0,3)$

The x-intercept is the point $(1,0)$

For $f^{-1}(x)=-\frac{1}{3}x+1$

The y-intercept is the point $(0,1)$

The x-intercept is the point $(3,0)$

plot the intercepts both functions to graph the linear equations

see the attached figure

Answer 2

If you take the original equation, it's in y equals mx +b form so y intercept is 3 and the slope is negative 3. the inverse equation is when you put x in for y and vise versa. so x equals -3y +3. then solve for y and graph the new y =mx+b equation.