Question

How do I graph the function and it's inverse

Answer 1

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.

Answer 2

The graph both functions in the attached figure

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=-(1)/(3)x+1`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=-(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)=-(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