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Chapter 3: Problem 63

If \(k(x)=3\), evaluate \(k(100)\).

Short Answer

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Step by step solution

01

Understand the Function

The function given is constant, meaning it does not depend on the variable. The function is given by \(k(x)=3\).
02

Substitute the Value

To evaluate \(k(100)\), substitute 100 into the function: \(k(100)\).
03

Evaluate the Function

Since the function \(k(x)\) is constant and equals 3 for any value of \(x\), \(k(100)\) will also be 3.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

constant function
A constant function is a special type of function where the output value remains the same, regardless of the input value of the variable. In mathematical terms, if we have a function defined as something like \( k(x) = c \), where \( c \) is a constant, this means that no matter what value of \( x \) we plug into the function, the result will always be \( c \).
This concept is important because it simplifies calculations and understanding how functions behave. For example, in the exercise provided, \( k(x) = 3 \) is a constant function, which means that for any input \( x \), the output will always be 3.
function evaluation
Function evaluation refers to the process of determining the output value of a function for a specific input value. In simpler terms, it is about finding the result of the function when you replace the variable with a given value.
When evaluating functions, it is important to understand the nature of the function. For example, in our exercise, evaluating \( k(100) \) for the constant function \( k(x) = 3 \) is straightforward. You just recognize that no matter what the input is, the output will be 3, so \( k(100) \) is simply 3.
Evaluating more complex functions might require additional steps, such as arithmetic operations or even solving equations.
substitution
Substitution is the process of replacing a variable in a function with a specific value. It helps in evaluating functions to find specific outcomes based on different inputs.
For instance, in the exercise, we need to find the value of \( k(100) \) where \( k(x) = 3 \). This is done by substituting \( 100 \) into the function in place of the variable \( x \).
In this case, since the function is constant, substituting \( 100 \) into \( k(x) \) does not change the output: \( k(100) = 3 \).
Substitution is a crucial skill for solving various mathematical problems and is often used in algebra, calculus, and other areas of math.

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