CPM Homework Help : PC3 Problem 2-102

Given $f(x)=x^2-2x+5$ and $g(x)=x-3$ , for what value(s) of $x$ does $f(g(x))=8$ ?

Hint:

Substitute the $g$ function into the $f$ function and set it equal to $8$ .

Step 1:

$f(x-3)=8$

Step 2:

$(x-3)^2-2(x-3)+5=8$