Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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0:50 minutes

Problem 60

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(k)

Verified step by step guidance

Identify the function g(x) which is given as g(x) = -x^2 + 4x + 1.

Replace the variable x in the function g(x) with k to find g(k).

Substitute k into the function: g(k) = -k^2 + 4k + 1.

Simplify the expression if necessary. In this case, the expression is already in its simplest form.

The expression for g(k) is now fully determined as g(k) = -k^2 + 4k + 1.

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Key Concepts

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

Function Notation

Function notation is a way to represent mathematical functions. In this context, ƒ(x) and g(x) denote two different functions, where 'x' is the input variable. Understanding how to read and interpret function notation is essential for evaluating functions at specific values, such as g(k).

Evaluating Functions

Evaluating a function involves substituting a specific value for the variable in the function's expression. For example, to find g(k), you replace 'x' in the function g(x) with 'k'. This process allows you to compute the output of the function for that particular input.

Simplifying Expressions

Simplifying expressions is the process of reducing a mathematical expression to its simplest form. This may involve combining like terms, factoring, or performing arithmetic operations. In the context of finding g(k), simplifying the resulting expression after substitution is crucial for presenting the final answer clearly.