Originally Posted by
topsquark If your book told you the answer is a = 8/3, then the book is wrong.
You have
$\displaystyle f(x + 6) = 2x + a$
and you want
$\displaystyle f(a) = 20$.
Well, if $\displaystyle f(x + 6) = 2x + a$ then
Let $\displaystyle y = x + 6 \implies x = y - 6$ so
$\displaystyle f(y) = 2(y - 6) + a$
$\displaystyle f(y) = 2y - 12 + a$
We want $\displaystyle f(a) = 20$, so
$\displaystyle f(a) = 2a - 12 + a = 20$
$\displaystyle 3a - 12 = 20$
$\displaystyle 3a = 32$
$\displaystyle a = \frac{32}{3}$
-Dan