Given the following functions:
f(x) = x² + 5
g(x) = -x + 5
Let's find (g - f)(-6),
[tex]\text{ \lparen g - f\rparen\lparen x\rparen = g\lparen x\rparen - f\lparen x\rparen}[/tex]
Let's first find g(-6),
[tex]\begin{gathered} \text{ g\lparen x\rparen = -x + 5} \\ \text{ g\lparen-6\rparen = -\lparen-6\rparen + 5} \\ \text{ g\lparen-6\rparen = 6 + 5} \\ \text{ g\lparen-6\rparen = 11} \end{gathered}[/tex]
Next, let's find f(-6),
[tex]\begin{gathered} \text{ f\lparen x\rparen= x}^2\text{ + 5} \\ \text{ f\lparen-6\rparen= \lparen-6\rparen}^2\text{ + 5} \\ \text{ f\lparen-6\rparen = 36 + 5} \\ \text{ f\lparen-6\rparen = 41} \end{gathered}[/tex]
Now, (g - f)(-6),
[tex]\begin{gathered} \text{ \lparen g - f\rparen\lparen-6\rparen = g\lparen-6\rparen - f\lparen-6\rparen} \\ \text{ \lparen g - f\rparen\lparen-6\rparen = 11 - 41} \\ \text{ \lparen g - f\rparen\lparen-6\rparen = -30} \end{gathered}[/tex]
Therefore, (g - f)(-6) = -30
