Perform the requested operation or operations. f(x) = 4x + 6, g(x) = 5x². Find (f + g)(x).

Solution:

A function that depends on any other function is called a composite function.

A composite function is created by composing one function within another function.

Given, f(x) = 4x + 6

g(x) = 5x²

We have to find (f + g)(x)

(f+g)(x) = f(x) + g(x)

Substituting the values

(f + g)(x) = 4x + 6 + 5x²

(f + g)(x) = 5x² + 4x + 6

Therefore, the solution to (f + g)(x) is 5x² + 4x + 6.

Example:

Perform the requested operation or operations. f(x) = 5x + 3, g(x) = 5x. Find (f + g)(x).

Solution:

Given, f(x) = 5x + 3

g(x) = 5x

We have to find (f + g)(x)

(f + g)(x) = f(x) + g(x)

Substituting the values

(f + g)(x) = 5x + 3 + 5x

(f + g)(x) = 10x + 3

Therefore, the solution to (f + g)(x) is 10x + 3.

---

Perform the requested operation or operations. f(x) = 4x + 6, g(x) = 5x². Find (f + g)(x).

Summary:

If f(x) = 4x + 6 and g(x) = 5x², then (f + g)(x) = 5x² + 4x + 6.