Respuesta :
Answer:
1. f(1)=-1 and g(-1)=-2.
2. (gof)(1)=-2.
3. (gofof)(-1)=-2
4. (fog)(3)=-1
Step-by-step explanation:
The given functions are defined as
f={(-2,3),(-1,1),(0,0),(1,-1), (2,-3)}
g={(-3,1),(-1,-2), (0, 2),(2, 2),(3,1)}
1.
The value of function f at x=1 is -1, So, f(1)=-1.
The value of function g at x=-1 is -2, So, g(-1)=-2.
Therefore the value of f(1) is -1 and the value of g(-1) is -2.
2.
[tex](g\circ f)(1)=g(f(1))[/tex] [tex][\because (g\circ f)(x)=g(f(x))][/tex]
[tex](g\circ f)(1)=g(-1)[/tex] [tex][\because f(1)=-1][/tex]
[tex](g\circ f)(1)=-2[/tex] [tex][\because g(-1)=-2][/tex]
Therefore the value of (gof)(1) is -2.
3.
[tex](g\circ f\circ f)(-1)=(g\circ f)(f(-1))[/tex] [tex][\because (g\circ f)(x)=g(f(x))][/tex]
[tex](g\circ f\circ f)(-1)=(g\circ f)(1)[/tex] [tex][\because f(-1)=1][/tex]
[tex](g\circ f\circ f)(-1)=-2[/tex] [tex][\because \text{From part 2}, (g\circ f)(1)=-2][/tex]
Therefore the value of (gofof)(1) is -2.
4.
[tex](f\circ g)(3)=f(g(3))[/tex] [tex][\because (f\circ g)(x)=f(g(x))][/tex]
[tex](f\circ g)(3)=f(1)[/tex] [tex][\because g(3)=1][/tex]
[tex](f\circ g)(3)=-1[/tex] [tex][\because f(1)=-1][/tex]
Therefore the value of (fog)(3) is -1.
