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 56
Chapter 3, Problem 56

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(-7/3)

Verified step by step guidance
1
Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
Substitute the value x = -\(\frac{7}{3}\) into the function ƒ(x). This means replacing every x in the expression with -\(\frac{7}{3}\).
Write the substitution explicitly: ƒ\(\left\)(-\(\frac{7}{3}\[\right\)) = -3 \(\times\) \(\left\)(-\(\frac{7}{3}\]\right\)) + 4.
Multiply -3 by -\(\frac{7}{3}\) carefully, remembering that multiplying two negatives results in a positive.
After the multiplication, add 4 to the result to simplify the expression and find ƒ\(\left\)(-\(\frac{7}{3}\)\(\right\)).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

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

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula and simplifying to find the output. For example, to find ƒ(-7/3), replace x with -7/3 in ƒ(x) and simplify the expression.
Recommended video:
4:26
Evaluating Composed Functions

Linear Functions

A linear function has the form ƒ(x) = mx + b, where m and b are constants. Its graph is a straight line, and evaluating it involves simple arithmetic operations like multiplication and addition.
Recommended video:
06:07
Linear Inequalities

Simplifying Rational Expressions

When substituting fractions into functions, it's important to carefully perform arithmetic with rational numbers. Simplifying involves reducing fractions and combining terms to express the result in simplest form.
Recommended video:
Guided course
05:07
Simplifying Algebraic Expressions
Related Practice
Textbook Question

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

760
views
Textbook Question

Graph each function. Give the domain and range. g(x)=[[2x-1]]

802
views
1
rank
Textbook Question

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

616
views
Textbook Question

For each line, (a) find the slope and (b) sketch the graph. 4x + 3y = 12

554
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)=x2−4x+2ƒ(x)=x^2-4x+2

900
views
Textbook Question

Graph each function. Give the domain and range. ƒ(x)=[[2x]]

1351
views