Question

Jim was given three functions and asked to determine ƒ + (g ○ h). The functions were ƒ (x) = x2, g(x) = 3x + 1, and h(x) = 2x. Jim started by writing the problem as (ƒ + (g ○ h))(x) = x2 + 2(3x + 1). What was Jim's mistake? What is the correct solution?

Answer 1

[f + (g o h)](x) = x² + 6x + 1

Explanation:

Given functions are,f(x) = x²

g(x) = 3x + 1

h(x) = 2x

Now we have to find the value of composite function [f + (g o h)](x).

(g o h)(x) = g[h(x)]

= 3(2x) + 1

= 6x + 1

[f + (g o h)](x) = f(x) + (g o h)(x)

= x² + 6x + 1

But Jim got the answer as,

[f + (g o h)](x) = x² + 2(3x + 1)

= x² + 6x + 2

Therefore, Jim's answer was incorrect.

Correct answer will be [f + (g o h)](x) = x² + 6x + 1