solution:
case: functions
Method:
a)
[tex]\begin{gathered} (f\circ g)(5) \\ f(g(5)) \\ \Rightarrow g(5)=-2 \\ Hence \\ f(g(5)) \\ \Rightarrow f(-2)=-5(-2)^2-4(-2)-5 \\ f(-2)=-5\times4-4(-2)-5 \\ f(-2)=-20+8-5 \\ f(-2)=-17 \end{gathered}[/tex]
b)
[tex]\begin{gathered} (g\circ f)(0) \\ g(f(0)) \\ \Rightarrow f(0)=-5(0)^2-4(0)-5 \\ f(0)=-5 \\ Hence \\ g(f(0)) \\ \Rightarrow g(-5) \\ g(-5)=-4x+2 \\ g(-5)=-4(-5)+2 \\ g(-5)=20+2 \\ g(-5)=22 \end{gathered}[/tex]
Final answer:
[tex]\begin{gathered} a)\text{ }(f\circ g)(5)=-17 \\ b)\text{ }(g\circ f)(0)=22 \end{gathered}[/tex]
