linear functions

[jinx24]

I am really stumped on this one.

"Find a linear function f(x) = mx + b such that m is positive and (f o f)(x) = 9x + 4."

I found the composition, 81x + 40. I don't know where to take it from here.


Thanks!

 

[Matt]

(f o f)(x) = 9x + 4.

I found the composition, 81x + 40.

?

 

[pka]

\(\displaystyle \L
\begin{eqnarray*}{l }
f(x) & = & mx + b \\
& = & m(mx + b) + b \\
& = & m^2 x + mb + b \\
& = & 9x + 4\quad \Rightarrow \quad m^2 = 9 \\
\end{array}\)

Now solve for m&b. Be careful! There are two values for m and two for b.

 

[jinx24]

Is that not right?

(f o f)(x) = 9x +4

9x + 4 ---> 9(9x + 4) + 4
= 81x + 36 + 4
= 81x + 40

 

[jinx24]

Thanks, pka...that makes much more sense now. I will go work on it and come back.

 

[jinx24]

Well, I thought what pka said made more sense. I am just as confused. How did pka get from "(m^2)x + mb +b" to "9x + 4 ----> m^2 = 9" ?

I understand that m^2 is 9, therefore m = 3. Which equation do I use to solve for "b"

Thanks.

 

[stapel]

How did pka get from "(m^2)x + mb +b" to "9x + 4 ----> m^2 = 9"

What is the coefficient of "x" in "m²x + mb + b"?

What is the coefficient of "x" in "9x + 4"?

For the two expressions to be equal, what must be true of the coefficients?

Which equation do I use to solve for "b"

"Which" of what equations?

Why not just follow the exact same procedure (comparing coefficients) as for finding "m"?

Eliz.