Question

I do not know how to set this up to solve. please help. see attached.

Answer 1

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,

$\begin{gathered} f(x)=4-x \\ f(5)=4-5 \\ f(5)=-1 \end{gathered}$

for g(3), 3 lies on the interval x>-2.

$\begin{gathered} g(x)=x^2+8x-1 \\ g(3)=(3)^2+8(3)-1 \\ g(3)=9+24-1 \\ g(3)=32 \end{gathered}$

After the corresponding values are found the expression can be writen as

$\begin{gathered} 4f(5)+g(3)=4\cdot(-1)+(32) \\ then, \\ -4+32=28 \end{gathered}$

The correct answer is 28.