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

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 11

Chapter 3, Problem 11

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

Verified step by step guidance

Understand that (ƒ+g)(x) means you add the functions ƒ(x) and g(x) together, so (ƒ+g)(x) = ƒ(x) + g(x).

Write the expressions for ƒ(x) and g(x): ƒ(x) = x^2 + 3 and g(x) = -2x + 6.

Add the two functions together: (ƒ+g)(x) = (x^2 + 3) + (-2x + 6).

Simplify the expression by combining like terms: (ƒ+g)(x) = x^2 - 2x + (3 + 6).

Evaluate the simplified expression at x = 3 by substituting 3 for x: (ƒ+g)(3) = 3^2 - 2(3) + 9.

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 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 expression and simplifying to find the output.

Function Addition

The sum of two functions, (ƒ + g)(x), is defined by adding their outputs for the same input x. This means (ƒ + g)(x) = ƒ(x) + g(x), combining the expressions before evaluating at a given value.

Substitution and Simplification

To find (ƒ + g)(3), substitute x = 3 into both ƒ(x) and g(x), then add the results. Simplifying the expressions after substitution yields the final numerical value.

Recommended video:

Guided course

5:48

Solving Systems of Equations - Substitution

Related Practice

Textbook Question

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

836

views

Textbook Question

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

$(ƒ + g) (- 5)$

1183

views

Textbook Question

Determine whether each relation defines a function. {(5,1),(3,2),(4,9),(7,8)}

839

views

Textbook Question

Determine whether each relation defines a function. {(8,0),(5,7),(9,3),(3,8)}

814

views

Textbook Question

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

759

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 (1,3), m = -2

847

views