SOLUTION: The function h(x) was used to generate the following code: 21,30,45,30,60,27,18,15,63,18,60,63 Decode this message if h(x)=(f+g)(x) and f(x)= 2x+1 g(x)= x+2 I'm lost, ho

Algebra ->  Functions -> SOLUTION: The function h(x) was used to generate the following code: 21,30,45,30,60,27,18,15,63,18,60,63 Decode this message if h(x)=(f+g)(x) and f(x)= 2x+1 g(x)= x+2 I'm lost, ho      Log On


   

Question 91371: The function h(x) was used to generate the following code:
21,30,45,30,60,27,18,15,63,18,60,63
Decode this message if h(x)=(f+g)(x) and f(x)= 2x+1 g(x)= x+2
I'm lost, how do I solve this?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
h%28x%29+=+%28f%2Bg%29%28x%29
f%28x%29+=+2x%2B1 and g%28x%29+=+x%2B2, so
%28f%2Bg%29%28x%29+=+%282x%2B1%29%2B%28x%2B2%29 = 3x%2B3
h%28x%29+=+3x%2B3
Now you want to set h(x) = to each of the numbers in your list, solve for x, then select the corresponding letter of the alphabet. I'll do the first few to get you started:
First letter:
3x%2B3+=+21 Subtract 3 from both sides.
3x+=+18 Divide both sides by 3.
x+=+6 The 6th letter of the alphabet is F. This is the first letter of the message.
2nd letter:
3x%2B3+=+30
3x+=+27
x+=+9 The 9th letter of the alphabet is I. This is the second letter of the message.
3rd letter:
3x%2B3+=+45
3x+=+42
x+=+14 The 14th letter of the alphabet is N. This is the 3rd letter of the message.
You should be able to finish this yourself.
If you are still having trouble, re-post the problem.