In order to find the missing values of f(5) and g(3), we have to use the piecewise functions, for that we look at the intervals for f(x) and g(x) where 5 and 3 are ubicated respectively.
for f(5), 5 lies on the interval x≥3.
then,
[tex]\begin{gathered} f(x)=4-x \\ f(5)=4-5 \\ f(5)=-1 \end{gathered}[/tex]
for g(3), 3 lies on the interval x>-2.
[tex]\begin{gathered} g(x)=x^2+8x-1 \\ g(3)=(3)^2+8(3)-1 \\ g(3)=9+24-1 \\ g(3)=32 \end{gathered}[/tex]
After the corresponding values are found the expression can be writen as
[tex]\begin{gathered} 4f(5)+g(3)=4\cdot(-1)+(32) \\ then, \\ -4+32=28 \end{gathered}[/tex]
The correct answer is 28.
