SOLUTION: 1) Find the inverse of f(x)=7x+11 2)How much money will there be in an account at the end of 7 years if $8000 is deposited at 5% interest compounded semi-annually? Round to th

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1) Find the inverse of f(x)=7x+11 2)How much money will there be in an account at the end of 7 years if $8000 is deposited at 5% interest compounded semi-annually? Round to th      Log On


   

Question 1139824: 1) Find the inverse of f(x)=7x+11

2)How much money will there be in an account at the end of 7 years if $8000 is deposited at 5% interest compounded semi-annually? Round to the nearrest cent as needed.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
(1)

f%28x%29=7x%2B11

Inverse - -
7y%2B11=x
7y=x-11
y=%28x-11%29%2F7

highlight%28f%5E%28-1%29%28x%29=%28x-11%29%2F7%29

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


The other tutor showed a general method for finding the inverse of a function (if there is one): switch the x and y and solve for the new y.

You should know this method, because it will always find an inverse if there is one.

But here is a quick way to find the inverse of a function for many relatively simple functions.

This method is based on the idea that an inverse function "gets you back where you started". For an inverse function to get you back where you started, it has to perform the opposite operations, and in the opposite order, as compared to the original function.

In your example, the function says "multiply the input by 7 and then subtract 11".

So the inverse function has to say "add 11 and then divide by 7": %28x%2B11%29%2F7

(2) Annual interest rate of 5% means a semi-annual interest rate of 2.5%; 7 years means the interest is compounded 7*2 = 14 times. So

8000%281%2B.025%29%5E14

Use a calculator....