## How Do You Evaluate a Function? II

*This post about how to evaluate a function is part of a series of posts to help you prepare for the Advanced Algebra and Functions part of the Accuplacer test.*

## Question

For the function

what is the value of ?

A.

B.

C.

D.

## Solution

** f(x-1)** is what you get when you replace

**with**

*x***in . That is called “evaluating the function for**

*x*-1*x*-1

**.**”

### Sidebar: Function Notation

In algebra, usually when you write two things side by side with one of them in parentheses, that means you multiply those two things together:

So no one can blame you for thinking ** f(x)** means

**multiplied by**

*f**. But math notation, like other kinds of language, has exceptions.*

**x***f*(

*x*) means function

*f*, carried out on

**. And f(something else) means function**

*x**f*carried out on something else. For example, say function

*g*is defined as . That means ; ; and means (whatever * means).

It gets interesting when the parentheses in the function definition contain a function. For example, if , what is ? Well, we said that if you want to find , you insert * into the function definition. To find , insert into the function definition: if , then .

So to find ** f(x-1)** in the expression

insert ** x-1** wherever you see

**. You should get:**

*x*That’s answer choice B.

Usually an answer like this would be expressed as , but this question is multiple choice so you go with what you’ve got.

Another example of how to evaluate a function is here.

This question is similar to question number 13 in the sample questions for the Accuplacer Advanced Algebra and Functions test.