Question 1149579
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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
<font color=blue>2mx</font>+<font color=green>m+b</font> = <font color=blue>6x</font>+<font color=green>2</font>


Equating the two separate pieces has us see that
<font color=blue>2mx</font> = <font color=blue>6x</font>
2m = 6
m = 3


and also,
<font color=green>m+b</font> = <font color=green>2</font>
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)
<font color=red size=4>f(x) = 3x-1</font>


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.
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