SOLUTION: Write an equation for the inverse of the given​ one-to-one function. f(x) = (5x+4)/(7)

Algebra ->  Functions -> SOLUTION: Write an equation for the inverse of the given​ one-to-one function. f(x) = (5x+4)/(7)       Log On


   

Question 1097369: Write an equation for the inverse of the given​ one-to-one function.
f(x) = (5x+4)/(7)
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
This was already answered.


What is f?
started with x, multiplied by 5, added 4, divided by 7.

The inverse is the undoing of all that.
f%5E-1%28x%29=%28%28x%29%2A%287%29-4%29%2F5------f%5E-1%28x%29=%287x-4%29%2F5

OR

%285y%2B4%29%2F7=x
5y%2B4=7x
5y=7x-4
y=%287x-4%29%2F5

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

The problem:

Given the function y+=+%285x%2B4%29%2F%287%29, find the inverse.

(1) Algebraic solution: Switch the x and y in the equation and solve for the new y.

y+=+%285x%2B4%29%2F%287%29
x+=+%285y%2B4%29%2F%287%29
7x+=+5y%2B4
7x-4+=+5y
%287x-4%29%2F5+=+y
or
y+=+%287x-4%29%2F5


(2)Finding the inverse by understanding that the inverse has to "un-do" what the given function does.

Look at the steps of what is done to the input x to get y in the given function:
a) multiply by 5
b) add 4
c) divide by 7

The inverse function has to un-do all that, so it has to do the opposite operations in the opposite order:
a) multiply by 7: x becomes 7x
b) subtract 4: 7x becomes 7x-4
c) divide by 5: 7x-4 becomes %287x-4%29%2F5

So again we have the same inverse function: %287x-4%29%2F5