Answer:
[tex]\begin{equation*} g(d)-f(d)=-d^2-d-2 \end{equation*}[/tex]Explanation:
Given:
[tex]\begin{gathered} f(x)=x^2+4 \\ g(x)=-x+2 \end{gathered}[/tex]To find:
[tex]g(d)-f(d)[/tex]We can find g(d) by substituting x in g(x) with d, so we'll have;
[tex]g(d)=-d+2[/tex]We can find f(d) by substituting x in f(x) with d, so we'll have;
[tex]f(d)=d^2+4[/tex]We can now go ahead and subtract f(d) from g(d) and simplify as seen below;
[tex]\begin{gathered} g(d)-f(d)=(-d+2)-(d^2+4)=-d+2-d^2-4=-d^2-d+2-4 \\ =-d^2-d-2 \\ \therefore g(d)-f(d)=-d^2-d-2 \end{gathered}[/tex]Therefore, g(d) - f(d) = -d^2 - d -2