Question

Given f(x) = 3x and g(x) = 3x2 + 1, find the following expressions. 1

(a) (fog)(4)
(b) (gof)(2)
(c) (f of)(1)
(d) (gog)(0)

Answer 1

Composite functions of f(x) and g(x) were calculated, with results being (a) 147, (b) 109, (c) 9, and (d) 4.

Step-by-step explanation:

The question requires finding composite functions for f(x) = 3x and g(x) = 3x2 + 1.

1. (f ∘ g)(4) requires applying g to 4, then f to the result of g(4). So, g(4) = 3(4)2 + 1 = 3(16) + 1 = 48 + 1 = 49. Then apply f to get f(49) = 3(49) = 147.
2. (g ∘ f)(2) requires applying f to 2, then g to the result of f(2). So, f(2) = 3(2) = 6. Then apply g to get g(6) = 3(6)2 + 1 = 3(36) + 1 = 108 + 1 = 109.
3. (f ∘ f)(1) is the application of f to 1, and then f again to the result. So, f(1) = 3(1) = 3. Then apply f again to get f(3) = 3(3) = 9.
4. (g ∘ g)(0) requires applying g to 0, then g again to the result. So, g(0) = 3(0)2 + 1 = 0 + 1 = 1. Then apply g again to get g(1) = 3(1)2 + 1 = 3(1) + 1 = 3 + 1 = 4.

The answers to the expressions are (a) 147, (b) 109, (c) 9, and (d) 4.