Values of the composite function:
[tex](g\cdot f)(-1)=6[/tex]
[tex](g\cdot f)(0)=7[/tex]
[tex](f\cdot g)(-1)=3[/tex]
[tex](f\cdot g)(4)=2[/tex]
Step-by-step explanation:
Given two functions f(x) and g(x), their composite function is given by
[tex](f\cdot g)(x) = f(g(x))[/tex]
Which means using the output value of g(x) as input for f(x).
Let's start by computing
[tex](g\cdot f)(-1)[/tex]
First, we compute the value of f(-1), which is (from the graph)
f(-1) = 1
Now we use this value as input into g(x); we notice that at x = 1, the value of g(x) is 6, therefore:
[tex](g\cdot f)(-1)=6[/tex]
Now we evaluate
[tex](g\cdot f)(0)[/tex]
First, we compute the value of f(0), which is (from the graph)
f(0) = 0
Now we use this value as input into g(x); at x = 0, the value of g(x) is 7, therefore:
[tex](g\cdot f)(0)=7[/tex]
Now we evaluate
[tex](f\cdot g)(-1)[/tex]
First, we compute the value of g(-1), which is (from the graph)
g(-1) = 5
Now we use this value as input into f(x); at x = 5, the value of f(x) is 3, therefore:
[tex](f\cdot g)(-1)=3[/tex]
Finally we evaluate
[tex](f\cdot g)(4)[/tex]
First, we compute the value of g(4), which is (from the graph)
g(4) = 4
Now we use this value as input into f(x); at x = 4, the value of f(x) is 2, therefore:
[tex](f\cdot g)(4)=2[/tex]
Learn more about composite functions:
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