Question

1-3 Function Operations and Composition Jim was given three functions and asked to determine f + (gon). The functions were f (x) = x2 g(x) = 3x + 1, and h(x) = 2x. Jim started by writing the problem as (r + (gon))(x) = x2 + 2(3x + 1). What was Jim's mistake? What is the correct solution? O A Jim omitted the x in h(x): [ + (g = n)) = 7x2 + 2x B. Jim should have added f and g first; ( + (gon)) = 4x2 + 6x + 1 O C. Jim incorrectly performed h og instead of goh: (f + g - h)) = x2 + x + 1. OD D. Jim did not follow the order of operations, I + (g o h)) = x2 + 6x + 2.​

Answer 1

Explanation:

Given the functions:

f (x) = x^2

g(x) = 3x + 1

h(x) = 2x

We are to look for f + (goh)

First we need to get the composite function goh

goh = g(h(x))

g(h(x)) = g(2x)

To get g(2x) we will substitute x in g(x) as 2x as shown below:

Given g(x) = 3x+1

g(2x) = 3(2x)+1

g(2x) = 6x+1

f + goh = x² + (6x +1)

f + goh = x² + 6x +1

Jim wrote goh as 2(3x+1) instead of 3(2x) + 1. The composite function that Jim looked for was hog not goh.

The correct solution is f + goh = x² + 6x +1