ANSWERS
a) 5
b) 6
c) -2
d) -1
EXPLANATION
The composition of two functions is equivalent to,
[tex](g\circ f)(x)=g(f(x))[/tex]
a) To find (g o f)(4) we have to find g(f(4)). In the graph, we can see that the value of f(x) at x = 4 is -1,
[tex](g\circ f)(4)=g(f(4))=g(-1)[/tex]
Then, g(x) at x = -1 is 5.
Hence,
[tex](g\circ f)(4)=5[/tex]
b) Similarly,
[tex](g\circ f)(0)=g(f(0))[/tex]
f(x) at x = 0 is 1,
[tex]g(f(0))=g(1)[/tex]
And g(x) at x = 1 is 6.
Hence,
[tex](g\circ f)(0)=6[/tex]
c) In this case, first, we have to find the value of g(x),
[tex](f\circ g)(3)=f(g(3))[/tex]
The value of g(x) at x = 3 is 3,
[tex]f(g(3))=f(3)[/tex]
And the value of f(x) at x = 3 is -2.
Hence,
[tex](f\circ g)(3)=-2[/tex]
d) Similarly,
[tex](f\circ g)(4)=f(g(4))[/tex]
The value of g(x) at x = 4 is 4,
[tex]f(g(4))=f(4)[/tex]
And the value of f(x) at x = 4 is -1.
Hence,
[tex](f\circ g)(4)=-1[/tex]
