Let ƒ(x)=x2+3 and g(x)=-2x+6. Find each of the following. (ƒg)(4)

Ch. 2 - Graphs and Functions

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

All textbooks

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 15

Chapter 3, Problem 15

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒg)(4)

Verified step by step guidance

Understand that (ƒg)(4) means the composition of functions ƒ and g evaluated at 4, which is written as ƒ(g(4)). This means you first find g(4), then substitute that result into ƒ(x).

Calculate g(4) by substituting 4 into the function g(x) = -2x + 6. So, compute g(4) = -2(4) + 6.

Simplify the expression for g(4) to find its value. This will give you the input for the next step.

Substitute the value of g(4) into the function ƒ(x) = x^2 + 3. This means you replace x in ƒ(x) with the value you found for g(4).

Simplify the expression ƒ(g(4)) by squaring the value from g(4) and then adding 3, which will give you the final expression for (ƒg)(4).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Function Composition

Function composition involves applying one function to the result of another, denoted as (f∘g)(x) = f(g(x)). It means you first evaluate g at x, then use that output as the input for f. This concept is essential for understanding how to combine functions and evaluate them at specific values.

Evaluating Functions at a Given Input

Evaluating a function at a given input means substituting the input value into the function's formula and simplifying to find the output. For example, to find g(4), replace x with 4 in g(x) = -2x + 6 and simplify. This step is crucial before composing functions.

Polynomial and Linear Functions

Understanding the forms of polynomial functions like f(x) = x² + 3 and linear functions like g(x) = -2x + 6 helps in correctly substituting and simplifying expressions. Recognizing these types aids in performing arithmetic operations and function evaluations accurately.

Recommended video:

06:04

Introduction to Polynomial Functions

Related Practice

Textbook Question

Determine whether each relation defines a function. {(9,-2),(-3,5),(9,1)}

Textbook Question

Let $ƒ (x) = x^{2} + 3$ and $g (x) = - 2 x + 6$ . Find each of the following. See Example 1.

$(ƒ - g) (4)$

views

Textbook Question

Determine the intervals of the domain over which each function is continuous.

Textbook Question

Determine whether each relation defines a function. {(-3,1),(4,1),(-2,7)}

views

Textbook Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. center (0, 4), radius 4

views

Textbook Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-8,4), undefined slope

views