Question

Consider the following functions.$(x) = x2 + 9 and g(x) = -x + 6Step 2 of 4: Find g(a)-f(a). Simplify your answer.Answer8(a)-f(a)

Answer 1

The functions are given as,

`\begin{gathered} f(x)\text{ = x}^2+9 \\ g(x)\text{ = -x + 6} \end{gathered}`

f(a) is calculated as,

`f(a)\text{ = a}^2+9__\text{ \_\_\_\_\_\_\_\_\lparen1\rparen}_`

g(a) is calculated as,

`g(a)\text{ = -a + 6 \_\_\_\_\_\_\_\lparen2\rparen}`

Subtracting equation (1) from (2),

`\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}`

Thus the required answer is,