Question

If ( f ∘ g)(x) = x2 - 6x + 8 and g(x) = x - 3, what is f(x)?

Answer 1

$\bf \begin{cases} (f\circ g)(x)=x^2-6x+8\\\\ (f\circ g)(x)=f(~~g(x)~~)\\\\ g(x)=x-3\\ \end{cases} \\\\\\ \textit{now, one probability is }x^2-1 \\\\\\ f(x)=x^2-1\implies f(~~g(x)~~)=(x-3)^2-1 \\\\\\ f(~~g(x)~~)=(x^2-6x+9)-1\implies f(~~g(x)~~)=x^2-6x+8$