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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 78b
Chapter 3, Problem 78b

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

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Start with the given equation: \(x - 4y = 8\).
Rewrite the equation to express \(y\) as a function of \(x\). To do this, isolate \(y\) on one side: subtract \(x\) from both sides to get \(-4y = 8 - x\).
Divide both sides of the equation by \(-4\) to solve for \(y\): \(y = \frac{8 - x}{-4}\).
Simplify the expression for \(y\): \(y = -2 + \frac{x}{4}\).
To find \(f(3)\), substitute \(x = 3\) into the function: \(f(3) = -2 + \frac{3}{4}\).

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Key Concepts

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

Function Definition

A function defines a relationship where each input x corresponds to exactly one output y. In this problem, y is expressed as a function of x, meaning for each x-value, there is a unique y-value that satisfies the equation.
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Graphs of Common Functions

Solving for y in terms of x

To find y as a function of x, rearrange the given equation to isolate y on one side. This involves algebraic manipulation, such as adding, subtracting, or dividing terms, to express y explicitly in terms of x.
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Solving Logarithmic Equations

Evaluating the function at a specific value

Once y is expressed as a function of x, finding ƒ(3) means substituting x = 3 into the function and calculating the corresponding y-value. This step applies the function definition to a particular input.
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Evaluating Composed Functions
Related Practice
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

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

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Textbook Question

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

ƒ(x)=x3,g(x)=x2+3x−1ƒ(x)=x^3, g(x)=x^2+3x-1

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)(ƒ∘g)(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 (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