Question

Let :

f(x) = x + 7
g(x) = x2
h(x) = 1/x
Write an arithmetic expression for the function f∘g, and find the value of f∘g(5)
Write an arithmetic expression for the function g∘f, and find the value of g∘f(5)
Write an arithmetic expression for the function h∘h, and find the value of h∘h(5)
Write an arithmetic expression for the function g∘f∘h, and find the value of g∘f∘h(5)
Please do your own work.

Answer 1

1. 32
2. 144
3. 5
4. 1.44

Explanation:

For example, f∘g means f(g(x)), which means we replace x with g(x) in the expression for f(x). Here are the answers to your questions:

• f∘g(x) = f(g(x)) = (x2) + 7. To find f∘g(5), we plug in 5 for x: f∘g(5) = (52) + 7 = 25 + 7 = 32.
• g∘f(x) = g(f(x)) = (x + 7)2. To find g∘f(5), we plug in 5 for x: g∘f(5) = (5 + 7)2 = 122 = 144.
• h∘h(x) = h(h(x)) = 1/(1/x) = x. To find h∘h(5), we plug in 5 for x: h∘h(5) = 5.
• g∘f∘h(x) = g(f(h(x))) = g(f(1/x)) = g((1/x) + 7) = ((1/x) + 7)2. To find g∘f∘h(5), we plug in 5 for x: g∘f∘h(5) = ((1/5) + 7)2 = (1.2)2 = 1.44.