Question

Consider the following functions.f(x) = x²+ 5 and g(x) = -x+2Step 2 of 4: Find (g - f)(-6). Simplify your answer.

Answer 1

Given the following functions:

f(x) = x² + 5

g(x) = -x + 5

Let's find (g - f)(-6),

`\text{ \lparen g - f\rparen\lparen x\rparen = g\lparen x\rparen - f\lparen x\rparen}`

Let's first find g(-6),

`\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}`

Next, let's find f(-6),

`\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}`

Now, (g - f)(-6),

`\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}`

Therefore, (g - f)(-6) = -30