Question 84376
 help! i cant figure out what the book wants me to do: 
find the formula for the inverse of the function

f(x) = 3 - 6x

1. Substitute y for f(x)
2. Interchange x and y
3. Solve for y
4. Replace y by f<sup>-1</sup>(x)

Lets first graph the given line in dark red, so you'll understand
what the inverse is.

Plotting f(x) = 3 - 6x, which is the same as y = 3 - 6x

{{{graph(400,400,-10,10,-10,10,3-6x)}}}

Now let's draw the graph of y = x in green, which is called the
identity line, on the same set of axes. Draw it dotted
because it's actually not part of the function of its
inverse:

{{{graph(400,400,-10,10,-10,10,3-6x,x*sqrt(sin(5x))/sqrt(sin(5x)) )  }}}
  
If we get the correct inverse it should be a reflection of
the dark red curve across the green dotted line (pretending the dotted
line is a two way mirror.)

Following the rules:

f(x) = 3 - 6x

1. Substitute y for f(x)

   y = 3 - 6x

2. Interchange x and y

   x = 3 - 6y

3. Solve for y

  6y = 3 - x    

   y = (3 - x)/6

4. Replace y by f<sup>-1</sup>(x)

f<sup>-1</sup>(x) = (3-x)/6

Now let's graph that line blue and see:

{{{graph(400,400,-10,10,-10,10,3-6x,x*sqrt(sin(5x))/sqrt(sin(5x)),(3-x)/6 )  }}}
  
As you see the blue line is the reflection of the dark
red line across the green identity line y = x.  So 

f<sup>-1</sup>(x) = (3-x)/6

is the equation of correct inverse function

Edwin