Question

Find a function g(x) such that g(g(x)) =
6x − 8.
Need help..

Answer 1

Let's suppose \(g(x)\) is a line. Then it has for form: \[
g(x) = Ax+B
\]

Answer 2

Note: I'm not sure that \(g(x)\) is a line, it's just an educated guess for now.

Answer 3

In fact, I'm not even sure \(g(x)\) has a single solution. It may have many.

Answer 4

Anyway, the assumption would give us: \[
g(g(x)) = A(Ax+B)+B = A^2x + AB + B
\]

Answer 5

So we have: \[
A^2x + AB + B = 6x-8 \\
(A^2)x + (AB + B) = (6)x+(-8) \\
A^2 = 6, \quad AB + B = -8
\]Think you can solve for \(A\) and \(B\)?
@rashley284

Answer 6

but what is g(x)?

Answer 7

We said\[
g(x) = Ax+B
\]So if you solve for \(A\) and \(B\), then you have found \(g(x)\).

Answer 8

g(g(x))=6x-8 . I don't get it.

Answer 9

@rashley284

Okay, I'll try to explain better.
We're going to assume that \(g(x)\) could be a line.
If it is a line, then it has the following form: \[
y = mx+b
\]Does this make sense so far?

Answer 10

If we assume that \(g(x)\) is a line, then we need to find it's slope and intercept. \[
g(x) = mx+b
\]For now, we will just keep them as variables \(m\) and \(b\).

Answer 11

@rashley284 Do you follow?

Answer 12

yes. . i get it now. Thank you.

Answer 13

Do I need to explain it anymore?

What answer are you getting?

Answer 14

so the slope is 6 and the y-intercept is (0,-8)? @wio