Skip to main content
Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 52
Chapter 3, Problem 52

Find the value of the function for the given value of x.
f(x)={3if 0<x≤410−2[[5−x]]if x>4, for , for x=6.2f(x)=\(\begin{cases}\)3 & \(\text{if }\)0<x\(\leq\)4\\ 10-2[\(\left\]\lbrack\)5-x]\(\right\[\rbrack\) & \(\text{if }\)x>4,\(\text{ for }\]\end{cases}\),\(\text{ for }\)x=6.2

Verified step by step guidance
1
First, carefully read the piecewise function definition to understand the different cases for ƒ(x). It seems the function has different values depending on the value of x.
Identify the value of x given in the problem, which is x = 6.2, and determine which part of the piecewise function applies to this value.
Check the conditions in the piecewise function to see where x = 6.2 fits. For example, if the function is defined as ƒ(x) = 3 for x < 4, and some other value for x ≥ 4, then since 6.2 is greater than 4, you will use the second part of the function.
Once you identify the correct piece of the function for x = 6.2, substitute x = 6.2 into that expression or use the given constant value for that interval.
Write down the value of ƒ(6.2) based on the substitution or the constant value from the piecewise function.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation and Evaluation

Function notation, written as ƒ(x), represents a rule that assigns each input x to exactly one output. Evaluating a function means substituting the given x-value into the function's rule to find the corresponding output.
Recommended video:
4:26
Evaluating Composed Functions

Piecewise Functions

A piecewise function is defined by different expressions depending on the input value's domain. Understanding which part of the function applies to the given x-value is essential for correctly evaluating the function.
Recommended video:
4:56
Function Composition

Domain and Input Values

The domain of a function is the set of all possible input values. Identifying whether the given x-value lies within the domain or specific intervals of a piecewise function helps determine which rule to use for evaluation.
Recommended video:
3:43
Finding the Domain of an Equation
Related Practice
Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=x2

808
views
Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

ƒ(x)=−x2ƒ(x)=-x^2

1109
views
Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=x2

562
views
Textbook Question

For each line, (a) find the slope and (b) sketch the graph. y = 2x - 4

626
views
Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(-3)

769
views
Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-1, 4), parallel to x+3y=5

1639
views