Function Notation Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
If f(x)=3x2−2x+1f(x) = 3x^2 - 2x + 1, find f(−2)f(-2).

Solution

  1. 1
    Replace every xx in the formula with −2-2: f(−2)=3(−2)2−2(−2)+1f(-2) = 3(-2)^2 - 2(-2) + 1.
  2. 2
    Evaluate: f(−2)=3(4)+4+1=12+4+1f(-2) = 3(4) + 4 + 1 = 12 + 4 + 1.
  3. 3
    f(−2)=17f(-2) = 17.

Answer

f(−2)=17f(-2) = 17
Function notation f(x)f(x) names the function (ff) and its input variable (xx). To evaluate f(a)f(a), substitute aa for every occurrence of xx in the expression. Be careful with signs when substituting negative values — use parentheses around the substituted value.

About Function Notation

Function notation f(x)f(x) is a shorthand that names a function (ff) and specifies its input (xx). Writing f(3)=10f(3) = 10 means that when the input is 3, the function produces the output 10. This notation is not multiplication.

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More Function Notation Examples

Example 2 medium

If [formula], find and simplify [formula].

Example 3 medium

If [formula] and [formula], find [formula] and [formula].

Example 4 hard

A function satisfies [formula] for all [formula], with [formula]. Find [formula], [formula], and [fo

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