Question

Please help!! Math | 25 points :)

Answer 1

Values of the composite function:

$(g\cdot f)(-1)=6$

$(g\cdot f)(0)=7$

$(f\cdot g)(-1)=3$

$(f\cdot g)(4)=2$

Step-by-step explanation:

Given two functions f(x) and g(x), their composite function is given by

$(f\cdot g)(x) = f(g(x))$

Which means using the output value of g(x) as input for f(x).

Let's start by computing

$(g\cdot f)(-1)$

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:

$(g\cdot f)(-1)=6$

Now we evaluate

$(g\cdot f)(0)$

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:

$(g\cdot f)(0)=7$

Now we evaluate

$(f\cdot g)(-1)$

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:

$(f\cdot g)(-1)=3$

Finally we evaluate

$(f\cdot g)(4)$

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:

$(f\cdot g)(4)=2$

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