Function Notation

Function Notation

This is a very useful way to express a function. Another way of writing \(y=2x+1\) is \(f(x) = 2x + 1\). We say “\(f\) of \(x\) is equal to \(2x + 1\)”. Any letter can be used, for example, \(g(x)\), \(h(x)\), \(p(x)\), etc.

1. Determine the output value:

   “Find the value of the function for \(x=-3\)” can be written as: “find \(f(-3)\)”.

   Replace \(x\) with \(-\text{3}\):

   \begin{align*} f(-3) & = 2(-3) + 1 = -5 \\ \therefore f(-3) & = -5 \end{align*}

   This means that when \(x = -3\), the value of the function is \(-\text{5}\).

2. Determine the input value:

   “Find the value of \(x\) that will give a \(y\)-value of \(\text{27}\)” can be written as: “find \(x\) if \(f(x)=27\)”.

   We write the following equation and solve for \(x\):

   \begin{align*} 2x + 1 & = 27 \\ \therefore x = & 13 \end{align*}

   This means that when \(x = 13\) the value of the function is \(\text{27}\).