The functions are given as,
[tex]\begin{gathered} f(x)\text{ = x}^2+9 \\ g(x)\text{ = -x + 6} \end{gathered}[/tex]
f(a) is calculated as,
[tex]f(a)\text{ = a}^2+9__\text{ \_\_\_\_\_\_\_\_\lparen1\rparen}_[/tex]
g(a) is calculated as,
[tex]g(a)\text{ = -a + 6 \_\_\_\_\_\_\_\lparen2\rparen}[/tex]
Subtracting equation (1) from (2),
[tex]\begin{gathered} g(a)\text{ - f\lparen a\rparen = \lparen-a+6\rparen- \lparen a}^2_+9) \\ g(a)\text{ - f\lparen a\rparen = -a + 6 - a}^2-9 \\ g(a)\text{ - f\lparen a\rparen= -a}^2\text{ - a - 3} \\ g(a)\text{ - f\lparen a\rparen= -\lparen a}^2+\text{ a + 3\rparen} \end{gathered}[/tex]
Thus the required answer is,
[tex]g(a)\text{ - g\lparen a}\operatorname{\rparen}\text{=-\lparen a}^2\text{ + a + 3\rparen}[/tex]
