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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 79b
Chapter 3, Problem 79b

An equation that defines y as a function of x is given. Find ƒ(3). y+2x2=3-x

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Start with the given equation: \(y + 2x^{2} = 3 - x\).
Isolate \(y\) on one side to express it as a function of \(x\): subtract \$2x^{2}\( from both sides to get \)y = 3 - x - 2x^{2}$.
Rewrite the function notation as \(f(x) = 3 - x - 2x^{2}\) to clearly show \(y\) as a function of \(x\).
To find \(f(3)\), substitute \(x = 3\) into the function: \(f(3) = 3 - (3) - 2(3)^{2}\).
Simplify the expression step-by-step by calculating the powers and performing the arithmetic to find the value of \(f(3)\).

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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 ƒ(x), represents a rule that assigns each input x to exactly one output y. Evaluating ƒ(3) means substituting x = 3 into the function's equation and calculating the corresponding y-value.
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Evaluating Composed Functions

Solving for y in Terms of x

To find ƒ(3), the equation must be rewritten to express y explicitly as a function of x. This involves isolating y on one side of the equation, often by performing algebraic operations like addition, subtraction, or division.
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Solving Logarithmic Equations

Substitution Method

After expressing y as a function of x, substitution involves replacing x with the given value (here, 3) to compute the specific output. This step is essential to find the function's value at a particular input.
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Related Practice
Textbook Question

An equation that defines y as a function of x is given. Find ƒ(3). x-4y=8

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Textbook Question

Given functions f and g, find (b)(g∘ƒ)(x)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

ƒ(x)=x+2,g(x)=x4+x2−4ƒ(x)=x+2, g(x)=x^4+x^2-4

Textbook Question

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

ƒ(x)=√(x−1),g(x)=3xƒ(x)=√(x-1), g(x)=3x

Textbook Question

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7.

ƒ(x)=√(x−1),g(x)=3xƒ(x)=√(x-1), g(x)=3x

Textbook Question

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=√(x-2), g(x)=2x

Textbook Question

Graph each function. See Examples 6–8 and the Summary of Graphing Techniques box following Example 9. ƒ(x)=-3(x-2)2+1