Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. g(-2)

Ch. 2 - Graphs and Functions

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

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Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 53

Chapter 3, Problem 53

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. g(-2)

Verified step by step guidance

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

To find $g(-2)$, substitute $x = -2$ into the function $g(x)$.

Replace every $x$ in the expression with $-2$: $g(-2) = -(-2)^2 + 4(-2) + 1$.

Simplify the expression step-by-step: first calculate $(-2)^2$, then multiply by the coefficients, and finally add all terms.

Write the simplified expression after performing all arithmetic operations to find the value of $g(-2)$.

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Key Concepts

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

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula and calculating the result. For example, to find g(-2), replace every x in g(x) with -2 and simplify the expression.

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents combined using addition, subtraction, and multiplication. Understanding how to work with polynomials, such as squaring terms and combining like terms, is essential for simplifying expressions like g(x) = -x² + 4x + 1.

Simplification of Algebraic Expressions

Simplification means reducing an expression to its simplest form by performing arithmetic operations and combining like terms. After substituting values into functions, simplifying ensures the final answer is clear and concise.

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Related Practice

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$ƒ (x) = 1 - x^{2}$

Textbook Question

For each line, (a) find the slope and (b) sketch the graph. 2y = -3x

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$ƒ (x) = 1 + 2 x^{2}$

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Textbook Question

Find the slope of each line, provided that it has a slope. 11x + 2y = 3

Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (1, 6), perpendicular to 3x+5y=1

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Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=√(x-3)