Question

Suppose g(x)=ax+b, where a and b are real constants. Find all possible pairs (a,b) such that we have g(g(x))=9x+28.
Show work or explain.

Answer 1

so g(x)=ax+b
can you find g(g(x))?

Answer 2

\[g(g(x)) =a ^{2}+ab+b\]

Answer 3

do you mean \[a^2x+ab+b\]?

Answer 4

yes

Answer 5

but g(g(x))=9x+28

so \[9x+28=a^2x+(ab+b)\]

Answer 6

\[a ^{2} x+ab+b=9x+28\]

Answer 7

If this expression is equal the other expression
then we must have the same amount of x's on both sides
and the same amount of constant on both sides