Question

I need help with this please!

Answer 1

The composite functions in this problem are given as follows:

• (h ∘ g)(b/3) = 0.444b² - 20.

• (h ∘ g)(a + 3) = 9a² + 63a + 107.

• (f ∘ f)(-2x) = -8x - 15.

What is the composite function of f(x) and g(x)?

The composite function of f(x) and g(x) is given by:

(f ∘ g)(x) = f(g(x)).

Hence, in the first item:

(h ∘ g)(x) = h(g(x)) = h(x² - 5) = 4(x² - 5) = 4x² - 20.

At x = b/3, the composite function is:

(h ∘ g)(b/3) = 4(b/3)² - 20 = 0.444b² - 20.

For the second item, the composite function is:

(h ∘ g)(a) = h(g(a)) = h(3a + 2) =

             = (3a + 2)² - 3 - (3a + 2)

             = 9a² + 12a + 4 - 3 - 3a - 2

             = 9a² + 9a - 1

Hence at a = a +3:

(h ∘ g)(a + 3) = 9(a + 3)² + 9(a + 3) - 1

                    = 9(a² + 6a + 9) + 9a + 27 - 1

                    = 9a² + 54a + 81 + 9a + 26

(h ∘ g)(a + 3) = 9a² + 63a + 107.

For item 3, the composite function is:

(f ∘ f)(-2x) = f(f(-2x)), hence:

• f(-2x) = 2(-2x) - 5 = -4x - 5.

• f(-4x - 5) = 2(-4x - 5) - 5 = -8x - 15.

Hence:

(f ∘ f)(-2x) = -8x - 15.

More can be learned about composite functions at brainly.com/question/10687170

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