Question

Consider the following functions.Step 2 of 4: Find (g-f)(-4). Simplify your answer.Answerf(x) = x² + 6 and g(x) = -x + 5(8-f)(-4)= |

Answer 1

Given

`f(x)=x^2+6\text{ }and\text{ }g(x)=-x+5`

To find:

`(g-f)(-4)`

Step-by-step explanation:

It is given that,

`f(x)=x^2+6\text{ }and\text{ }g(x)=-x+5`

That implies,

`\begin{gathered} (g-f)(x)=g(x)-f(x) \\ =-x+5-(x^2+6) \\ =-x-x^2+5-6 \\ =-x^2-x-1 \end{gathered}`

Therefore, for x=-4,

`\begin{gathered} (g-f)(-4)=-(-4)^2-(-4)-1 \\ =-16+4-1 \\ =-12-1 \\ =-13 \end{gathered}`

Hence, the value of (g-f)(-4)=-13.