SOLUTION:
Case: Functions
Method:
a)
Given that:
[tex]\begin{gathered} f(x)=7x-5 \\ f\circ f(-1) \\ \Rightarrow f(-1)=7(-1)-5 \\ f(-1)=-7-5 \\ f(-1)=-12 \\ \Rightarrow f(f(-1)) \\ f(-12)=7(-12)-5 \\ f(-12)=-84-5 \\ f(-12)=-89 \end{gathered}[/tex]
b)
[tex]\begin{gathered} g(x)=4-x^2 \\ g\circ g(4) \\ \Rightarrow g(4)=4-(4)^2 \\ g(4)=4-16 \\ g(4)=-12 \\ \Rightarrow g(g(4)) \\ g(-12)=4-(-12)^2 \\ g(-12)=4-144 \\ g(-12)=-140 \end{gathered}[/tex]
Final answer:
[tex]\begin{gathered} a)f\circ f(-1)=-89 \\ b)g\circ g(4)=-140 \end{gathered}[/tex]
