Question

Draw a machine diagram for the function. $$f(x)=\sqrt{x-1}$$

   Draw a machine diagram for the function.
$$f(x)=\sqrt{x-1}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 15

Instant Answer

Solved by Expert Josie Dalrymple

06/29/2020

Step 1

First, we need to subtract 1 from the input x. So, we'll have a box with the operation "subtract 1" and input x. The output of this box will be (x-1). Show more…

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Draw a machine diagram for the function. $$f(x)=\sqrt{x-1}$$

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Key Concepts

Function

A function is a rule that assigns each input exactly one output. In mathematics, it is represented by an expression that takes a value and transforms it based on a specific rule, such as f(x) = ?(x - 1). Understanding how this mapping works is fundamental in the study of functions and their properties.

Machine Diagram

A machine diagram is a visual representation of the operations that are applied to an input to produce an output. It typically consists of an input arrow, a processing box that indicates the operation performed (or operations in sequence), and an output arrow showing the result. This helps in visualizing the sequence of steps in function evaluation.

Composition of Operations

The function f(x) = ?(x - 1) involves a sequence of operations which is an example of function composition. First, the input is transformed by subtracting 1, and then the square root of the result is taken. Recognizing and ordering these operations is crucial to correctly understanding and evaluating the function.

Domain Considerations

When functions involve operations like the square root, it is necessary to consider the domain restrictions. In the case of f(x)=?(x-1), the expression under the square root must be non-negative, meaning that x - 1 ? 0. This directly impacts the set of allowable inputs for the function, emphasizing the importance of domain analysis in function evaluation.

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