JAMB 1988 · UME · Q16

If $g(y) = \frac{y - 3}{11} + \frac{11}{y^2 - 9}$ , what is $g(y + 3)$ ?

Worked solution (try it first)

Replace every $y$ by $y + 3$ : $g(y + 3) = \frac{(y + 3) - 3}{11} + \frac{11}{(y + 3)^2 - 9}$ .
The first top is $y$ .
Expand the bottom: $(y + 3)^2 - 9 = y^2 + 6y + 9 - 9$ , which is $y(y + 6)$ .
So $g(y + 3) = \frac{y}{11} + \frac{11}{y(y + 6)}$ , option A.