Suppose two function machines are hooked up in a sequence, so the output chute of machine g empties into the input hopper of machine f. Such a coupling of machines, which is defined if the range of g is a subset of the domain of f, is called the composition of f and g and can be written F(x) = f(g(x)). Suppose f is the doubling function f(x) = 2x and g is the "add 6" function g(x) = x + 6. Then F(4) = f(g(4)) = f(4 + 6) = f(10) = 2x 10 = 20. Evaluate f(g(x)) for x = 0, 1, 2, and 3.

Q: 3) Use the graph of f(x)-Сах to determine values for C and a -3 3

A: It is clear from graph that when x=0 , f(x)=3 , that is f(0)=3, using this , we can calculate C.

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A: y=f(x)= 3x-3 is a straight line and graph is

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A: We will draw a function which has two local maximum and one local minimum.

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Q: Use the graphs of f and g (see attached) to evaluate the composite function : (g ∘ f)(0)

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Q: If f is an even function, then f −1 exists.

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Q: Suppose two function machines are hooked up in a sequence, so the output chute of machine g empties…

A: Answer is below

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A: Rewrite the given function g as follows.