Question

Hey guys! help me ;;
given that:
g(g(x))=6x-8
how do we find g(x)?

Thanks guys love you all

Answer 1

I have the answer...
\[g(x)=\sqrt{6}x-\frac{ 8 }{ \sqrt{6}+1 }\]

but I have no idea how to get it

Answer 2

hey

Answer 3

I will try to think with ya

Answer 4

hmm..
is this calculus or algebra?

Answer 5

I guess we can try something since we have g(g(x)) is linear than g(x) is linear I believe
so we know g(x)=ax+b

Answer 6

\[g(x)=ax+b \\ g(g(x))=a(ax+b)+b \\ a^2x+ab+b=6x-8\]

Answer 7

so this mean
comparing both sides we have:
\[a^2=6 \\ \text{ and } \\ ab+b=-8\]

Answer 8

find a then you can find b

Answer 9

This is pre-calc, so algebra
Thank you so much freckles!

Answer 10

Np