Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 1

Chapter 3, Problem 1

Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$
$open paren f with hook positive g close paren times 2$

Verified step by step guidance

Understand that the notation $(\f+\g)(2)$ means you need to find the value of the function $(\f+\g)$ at $x=2$. The function $(\f+\g)(x)$ is defined as $\f(x) + \g(x)$.

Write the expression for $(\f+\g)(x)$ by adding the two given functions: $\f(x) = x + 1$ and $\g(x) = x^2$. So, $(\f+\g)(x) = (x + 1) + x^2$.

Substitute $x = 2$ into the expression: $(\f+\g)(2) = (2 + 1) + 2^2$.

Simplify the terms inside the parentheses and the exponent: $(2 + 1) = 3$ and $2^2 = 4$.

Add the simplified values together to get the final result: $3 + 4$.

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Key Concepts

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

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output. Evaluating a function at a specific value means substituting that value into the function's formula and simplifying to find the output.

Function Addition (Sum of Functions)

The sum of two functions (ƒ + g)(x) is defined as ƒ(x) + g(x). To evaluate (ƒ + g)(2), you find ƒ(2) and g(2) separately, then add the results together.

Substitution and Simplification

Substitution involves replacing the variable x with a given number in the function's expression. Simplification means performing arithmetic operations to reduce the expression to a single numerical value.

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Related Practice

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The circle with equation $x^{2} + y^{2} = 49$ has center with coordinates________ and radius equal to__________ .

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Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. P(3, -1), Q(-4, 5)

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Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x²? What is its domain?

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Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1ƒ(x)=x+1 and g(x)=x2g(x)=x^2 (ƒ+g)(2) (ƒ+g)(2)

Verified video answer for a similar problem:

Key Concepts

Function Notation and Evaluation

Function Addition (Sum of Functions)

Substitution and Simplification

Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$
$open paren f with hook positive g close paren times 2$