1) For the following problem: Let f={(-2,3),(-1,1),(0,0),(1,-1), (2,-3)} and let g-{-3,1),(-1,-2), (0, 2),(2, 2),(3,1)}.Find the following a) f(1) and g-1) b) (gof (1) c) (gofof)(-1) d) (fog)(3)

Accepted Solution

Answer:1. f(1)=-1 and g(-1)=-2.2. (gof)(1)=-2.3. (gofof)(-1)=-24. (fog)(3)=-1Step-by-step explanation:The given functions are defined asf={(-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.