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All courses Math I · F-IF.2 20 of 59
Use function notation, evaluate functions on their domains, and interpret notation in context.

Evaluate a function at a given input by substitution

Problem
Evaluate f(x)=3x+2 at x=4.
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Hint

Substitute 4 for x in f(x)=3x+2 before doing any arithmetic.

Function evaluation means replacing x with the given input and simplifying. For f(x)=3x+2, the input 4 must be used in the 3x term before adding 2.

Solution walkthrough

01

Identify the input

\[f(x)=3x+2,\quad~x=4\]

The question gives the function rule and the input. Evaluating the function means finding the output when x is 4.

02

Substitute into the rule

\[f(4)=3(4)+2\]

Replace x with 4 in the rule. The multiplication by 3 happens to the input before the 2 is added.

03

Simplify

\[3(4)+2=12+2=14\]

Follow order of operations: multiply 3 by 4 first, then add 2.

04

State the function value

\[f(4)=14\]

The output for input 4 is 14, so this is the value of the function at x=4.

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Another way

  1. Check the result by substituting 4 back into the rule: 3(4)+2 equals 14, so the output is consistent with the function rule.

!

Common mistake

A common mistake is to write 4 as the answer because 4 is the given input. The problem asks for the output after applying f(x)=3x+2.