SOLUTION: Find a linear function f(x) = mx + b such that m is positive and (f(f(x))= 9x + 4.
The answer is 3x + 1 and I can find this by trial and error. What I want to know is how to rea
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-> SOLUTION: Find a linear function f(x) = mx + b such that m is positive and (f(f(x))= 9x + 4.
The answer is 3x + 1 and I can find this by trial and error. What I want to know is how to rea
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Question 828946: Find a linear function f(x) = mx + b such that m is positive and (f(f(x))= 9x + 4.
The answer is 3x + 1 and I can find this by trial and error. What I want to know is how to reach this answer mathematically.
I've tried to do it this way: 9x + 4 = m(mx + b) + b = m^2(x) + bm + b but then I got stuck because I have too many unknowns to solve by the quadratic equation.
Could you please explain this to me?
Thanks in advance Found 2 solutions by oscargut, nerdybill:Answer by oscargut(2103) (Show Source):
You can put this solution on YOUR website! f(f(x) = m(mx + b) + b = m^2(x) + bm + b
.
And, they give you:
f(f(x)= 9x + 4
.
Your two equations are:
m^2 = 9 (equation 1)
and
bm+b = 4 (equation 2)
.
Solving equation 1:
m^2 = 9
m = 3
.
Substitute above into equation 2:
bm+b = 4
b(3)+b = 4
4b = 4
b = 1
.
solution then:
m = 3 and b = 1
so
f(x) = 3x+1
