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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 122
Chapter 3, Problem 122

Use the table to evaluate each expression, if possible.
(f/g)(0)(f/g) (0)
Table showing values of x with corresponding f(x) and g(x) for x = -1, 0, 1, and 3.

Verified step by step guidance
1
Identify the functions \( f(x) \) and \( g(x) \) from the given table. You need to find the values of \( f(0) \) and \( g(0) \) by looking up the corresponding outputs when \( x = 0 \).
Recall that the expression \( (f/g)(0) \) means \( \frac{f(0)}{g(0)} \). This is the value of the function \( f(x) \) divided by the value of the function \( g(x) \) at \( x = 0 \).
Check if \( g(0) \) is not zero because division by zero is undefined. If \( g(0) = 0 \), then \( (f/g)(0) \) is undefined and cannot be evaluated.
If \( g(0) \neq 0 \), substitute the values of \( f(0) \) and \( g(0) \) into the fraction \( \frac{f(0)}{g(0)} \).
Simplify the fraction if possible to express the final value of \( (f/g)(0) \).

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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 f(x) or g(x), represents the output of a function for a given input x. Evaluating a function at a specific value means substituting that value into the function's formula or table to find the corresponding output.
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Evaluating Composed Functions

Function Division (Quotient of Functions)

The quotient of two functions (f/g)(x) is defined as f(x) divided by g(x), provided g(x) ≠ 0. This operation combines two functions by dividing their outputs for the same input, and it is important to check the denominator to avoid division by zero.
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Multiplying & Dividing Functions

Using Tables to Evaluate Functions

When functions are given in table form, values of f(x) and g(x) at specific inputs are listed. To evaluate expressions like (f/g)(0), locate the values of f(0) and g(0) in the table and perform the required operation, ensuring the denominator is not zero.
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Evaluating Composed Functions
Related Practice
Textbook Question

Use the table to evaluate each expression, if possible.

(f−g)(3)(f-g)(3)

Textbook Question

Use the tables for ƒ and g to evaluate each expression.

(ƒ∘g)(3)(ƒ∘g)(3)

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Textbook Question

Let ƒ(x)=√(x−2)ƒ(x) = √(x-2) and g(x)=x2g(x) = x^2. Find each of the following, if possible. the domain of ƒ○gƒ ○ g

Textbook Question

Use the tables for ƒ and g to evaluate each expression.

(g∘ƒ)(−2)(g∘ƒ)(-2)

Textbook Question

Use the table to evaluate each expression, if possible.

(ƒ+g)(1)(ƒ+g)(1)

Textbook Question

The graphs of two functions ƒ and g are shown in the figures.

Find (ƒ∘g)(2)(ƒ∘g)(2).