SOLUTION: Given that f(x) = 6x – 3, find the following: (f^-1)(x) = f(2) = (f^-1)(-5) = Thank you!

Algebra ->  Functions -> SOLUTION: Given that f(x) = 6x – 3, find the following: (f^-1)(x) = f(2) = (f^-1)(-5) = Thank you!      Log On


   

Question 1117120: Given that f(x) = 6x – 3, find the following:
(f^-1)(x) =
f(2) =
(f^-1)(-5) =
Thank you!
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
6y-3=x
6y=x%2B3
y=x%2F6%2B1%2F2
f%5E%28-1%29%28x%29=x%2F6%2B1%2F2-----inverse function



Substitution for the other two items.

f%282%29=6%2A2-3=12-3=9
-
%28-5%29%2F6%2B1%2F2=-5%2F6%2B3%2F6=-2%2F6=-1%2F3

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Notice that another way to find the inverse of a simple function like this is to use the fact that an inverse function "un-does" what the function does.

The given function takes the input value, multiplies it by 6, and subtracts 3. To undo that, the inverse function needs to do the opposite operations in the opposite order: add 3 and divide by 6 --> %28x%2B3%29%2F6 which is of course the same as the answer from the other tutor, x%2F6%2B1%2F2.

Also notice that you don't need to find the inverse function to evaluate (f^-1)(-5).

When you are asked to evaluate (f^-1)(-5), the definition of an inverse function tells you that you are to find the value of the input value for which the given function value is -5:

6x-3+=+-5
6x+=+-2
x+=+-1%2F3

This is the same answer you get if you evaluate the inverse function at -5:

%28-5%2B3%29%2F6+=+-2%2F6+=+-1%2F3