What does (f*g)(x) denote?

What does (f*g)(x) denote?

• A. f(x) / g(x)
• B. f(x) times g(x)
• C. f(x) + g(x)
• D. f(g(x))

Answer: (B)

The expression (f*g)(x) means you take the value of f at x and multiply it by the value of g at x. In other words, (f*g)(x) = f(x) × g(x). This is the product of the two outputs for the same input. For example, if f(x) = 3x − 2 and g(x) = x + 4, then (f*g)(x) = (3x − 2)(x + 4) = 3x^2 + 10x − 8. It’s not f(g(x)) (that would be composition, applying g first, then f), and it’s not f(x) + g(x) or f(x) ÷ g(x). The star here indicates multiplication of the outputs.

The expression (fg)(x) means you take the value of f at x and multiply it by the value of g at x. In other words, (fg)(x) = f(x) × g(x). This is the product of the two outputs for the same input.

For example, if f(x) = 3x − 2 and g(x) = x + 4, then (f*g)(x) = (3x − 2)(x + 4) = 3x^2 + 10x − 8.

It’s not f(g(x)) (that would be composition, applying g first, then f), and it’s not f(x) + g(x) or f(x) ÷ g(x). The star here indicates multiplication of the outputs.