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

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

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

Answer: (C)

The expression (f/g)(x) means the quotient of the two functions evaluated at x. In other words, you take the value of f at x and divide it by the value of g at x, so it equals f(x) divided by g(x). This is only defined when g(x) ≠ 0, since you can’t divide by zero. It’s different from multiplying the outputs (f(x)·g(x)) and from composing the functions (f(g(x))). For example, if f(x) = x^2 and g(x) = x+1, then (f/g)(x) = x^2/(x+1).

The expression (f/g)(x) means the quotient of the two functions evaluated at x. In other words, you take the value of f at x and divide it by the value of g at x, so it equals f(x) divided by g(x). This is only defined when g(x) ≠ 0, since you can’t divide by zero. It’s different from multiplying the outputs (f(x)·g(x)) and from composing the functions (f(g(x))). For example, if f(x) = x^2 and g(x) = x+1, then (f/g)(x) = x^2/(x+1).