Textbook Question
Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(a+4)
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3. Functions
Intro to Functions & Their Graphs
1:29 minutesProblem 78b
Textbook Question
An equation that defines y as a function of x is given. Find ƒ(3). x-4y=8
Verified step by step guidance1
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: \(f(3) = -2 + \frac{3}{4}\).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey 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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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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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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