Given
[tex]f(x)=x^2+6\text{ }and\text{ }g(x)=-x+5[/tex]
To find:
[tex](g-f)(-4)[/tex]
Explanation:
It is given that,
[tex]f(x)=x^2+6\text{ }and\text{ }g(x)=-x+5[/tex]
That implies,
[tex]\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}[/tex]
Therefore, for x=-4,
[tex]\begin{gathered} (g-f)(-4)=-(-4)^2-(-4)-1 \\ =-16+4-1 \\ =-12-1 \\ =-13 \end{gathered}[/tex]
Hence, the value of (g-f)(-4)=-13.
