Algebra – Part 14: Product of Functions

Since we’ve been learning functions so far, this time is also about a form of function, known as the product of functions.

Description:

In algebra, the product of two functions is a new function that is obtained by multiplying the outputs of two given functions at each point in their domains.

Let’s say we have two functions f(x) and g(x). The product of these two functions is denoted by f(x) * g(x) or simply f(x)g(x) and is defined as:

(f * g)(x) = f(x) * g(x)

In other words, the value of the product of f and g at any given value of x is equal to the product of the values of f and g at that same value of x.

To find the product of functions, we simply multiply the two functions together, term by term. For example, if we have:

f(x) = 2x + 3
g(x) = x^2 – 1

Then, the product of these two functions, denoted as (f * g)(x) or f(x)g(x), is:

(f * g)(x) = (2x + 3)(x^2 – 1)

To find the value of the product at any given point, we simply substitute the value of x into the expression and simplify:

(f * g)(2) = (2(2) + 3)((2)^2 – 1)
= (4 + 3)(4 – 1)
= 21

So, the value of the product of f(x) and g(x) at x = 2 is 21.

Actual handwriting samples:

Sample 1:

Question: Find the product

f(x) = 3

g(x) = 4

Sample 2:

Question: Find the product

f(x) = x

f(x) = x + 1

And substitute 2 to x.

Sample 3:

Question: Find the product

(gh)(-3) = x

g(x) = x – 4

h(x) = x + 1

Sample 4:

Question: Find the product

(fg)(x)

f(x) = x + 7

g(x) = x – 5

Sample 5:

Question: Find the product

(f・g)(2)

f(x) = x^2 – 6

g(x) = 3x – 5