We are given the graphs of the functions g(x) and f(x)
a) (g+f)(1)
it can be written as
[tex](g+f)(1)=g(1)+f(1)[/tex]From the graph, we see that the values of the two functions at x = 1 are
g(1) = -1
f(1) = 1
[tex]\begin{gathered} (g+f)(1)=g(1)+f(1) \\ (g+f)(1)=-1+1 \\ (g+f)(1)=0 \end{gathered}[/tex]Therefore, (g+f)(1) = 0
b) (f-g)(-1)
It can be written as
[tex](f-g)(-1)=f(-1)-g(-1)[/tex]From the graph, we see that the values of the two functions at x = -1 are
g(-1) = 3
f(-1) = -1
[tex]\begin{gathered} (f-g)(-1)=f(-1)-g(-1) \\ (f-g)(-1)=-1-3 \\ (f-g)(-1)=-4 \end{gathered}[/tex]Therefore, (f-g)(-1) = -4
c) (g*f)(1)
It can be written as
[tex](g\cdot f)(1)=g(1)\cdot f(1)[/tex]From the graph, we see that the values of the two functions at x = 1 are
g(1) = -1
f(1) = 1
[tex]\begin{gathered} (g\cdot f)(1)=g(1)\cdot f(1) \\ (g\cdot f)(1)=-1\cdot1 \\ (g\cdot f)(1)=-1 \end{gathered}[/tex]Therefore, (g*f)(1) = -1
d) (f/g)(4)
It can be written as
[tex](\frac{f}{g})(4)=\frac{f(4)}{g(4)}[/tex]From the graph, we see that the values of the two functions at x = 4 are
f(4) = 0
g(4) = 0
[tex](\frac{f}{g})(4)=\frac{f(4)}{g(4)}=\frac{0}{0}=\text{undefined}[/tex]Therefore, (f/g)(4) is undefined.