Comp Functions

Notation §

(f $\circ$ g)(x) = f(g(x))

Rule §

• In this scenario if the value of g(x) is undefined then the value of f(x) is also undefined
• If g(x) returns a value then the value of f(x) may still be undefined depending on domain restrictions
• If (f $\circ$ g) g(x) is nested inside f(x)

Example §

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

f(x) = ? g(x) = ?

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

$\therefore$ f(g(x)) = f(x + 5) = log(x + 5)

Example 2 §

g(x) = x${}^2$ f(x) = $\sqrt{x}$

(f $\circ$ g)(2) = f(g(2)) = f(4) = 2