SOLUTION: help! i cant figure out what the book wants me to do: find the formula fort he inverse of the function f(x)=3-6x

Question 84376: help! i cant figure out what the book wants me to do:
find the formula fort he inverse of the function
f(x)=3-6x
Answer by Edwin McCravy(20086) (Show Source): You can put this solution on YOUR website!
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^-1(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

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:

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^-1(x)
f^-1(x) = (3-x)/6
Now let's graph that line blue and see:

As you see the blue line is the reflection of the dark
red line across the green identity line y = x. So
f^-1(x) = (3-x)/6
is the equation of correct inverse function
Edwin

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