Question 1149579: If f(2x+1)=6x+2 what is f(x)
Found 3 solutions by Edwin McCravy, jim_thompson5910, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! f(x) = 6x+2
To find f(2x+1), start with
f(x) = 6x+2
Take out all the x's and replace them all with empty parentheses ( )
f( ) = 6( )+2
Put 2x+1 inside the empty parentheses
f(2x+1) = 6(2x+1)+2
Simplify only the right side:
f(2x+1) = 12x+6+2
f(2x+1) = 12x+8
Edwin
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website!
I'm assuming f(x) is some linear function. If so, then,
f(x) = mx+b
m = slope
b = y intercept
Replace every x input with (2x+1) and simplify
f(x) = mx+b
f(2x+1) = m(2x+1) + b
f(2x+1) = m*2x+m*1 + b
f(2x+1) = 2mx+m+b
This is equal to 6x+2 since f(2x+1) = 6x+2 is given to us, so,
2mx+m+b = 6x+2
2mx+m+b = 6x+2
Equating the two separate pieces has us see that
2mx = 6x
2m = 6
m = 3
and also,
m+b = 2
3+b = 2 ... plug in m = 3
b = -1
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Therefore, m = 3 and b = -1, meaning we can say
f(x) = mx+b
f(x) = 3x+(-1)
f(x) = 3x-1
note that replacing every x with (2x+1) leads to...
f(x) = 3x-1
f(2x+1) = 3(2x+1)-1
f(2x+1) = 3(2x)+3(1)-1
f(2x+1) = 6x+3-1
f(2x+1) = 6x+2
which helps confirm our answer.
Answer by ikleyn(52782)  (Show Source):
You can put this solution on YOUR website! .
Right and CANONICAL way to do it is as follows.
Let "t" be new variable, t = 2x+1.
Then x =  .
Express 6x+2 via "t" :
6x+2 =  = 3*(t-1) + 2 = 3t - 3 + 2 = 3t-1.
Thus f(t) = 3t-1.
Here "t" is a "mute" / ("silent") variable. It can be replaced by ANY symbol in both sides simultaneously.
For example, it can be replaced by x. So
f(x) = 3x-1. ANSWER
Done, completed and explained.
This my post is the standard MANTRA to use for solution to each and every similar problem.
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// Mantra is called "mantra", because it DOES NOT ALLOW to change any word (!)
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