SOLUTION: Each of the functions below is one-to-one. Find the inverse function for each of them. (i) f(x) = 4x + 2 (ii) f(x) = 3x

Algebra ->  Functions -> SOLUTION: Each of the functions below is one-to-one. Find the inverse function for each of them. (i) f(x) = 4x + 2 (ii) f(x) = 3x       Log On


   

Question 1118903: Each of the functions below is one-to-one. Find the inverse function for each of them.
(i) f(x) = 4x + 2
(ii) f(x) = 3x

Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Each of the functions below is one-to-one.
Find the inverse function for each of them.
(i) f(x) = 4x + 2
f(x) = y
y = 4x + 2
swap x and y and solve for y
x = 4y + 2
4y = x - 2
y = 1%2F4x - 1%2F2
f%28x%5E-1%29 = 1%2F4x - 1%2F2
:
(ii) f(x) = 3x
y = 3x
x = 3y
y = 1%2F3x
f%28x%5E-1%29 = 1%2F3x

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


The formal algebraic process for finding the inverse of a function shown by the other tutor is something that is useful to know.

However, for simple functions like these, it is also instructive to find the inverses by using the understanding that an inverse function "un-does" what the function does. So an inverse function performs the opposite operations and in the opposite order, compared to the original function.

For your first example....

f(x) = 4x+2

The function (1) multiplies the input by 4 and (2) adds 2.
The inverse function must (1) subtract 2 and (2) divide by 4:
y+=+%28x-2%29%2F4

The second example is even easier. The second function only multiplies the input by 3; the inverse function only has to divide its input by 3:
y+=+x%2F3