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Chapter 3: Problem 61

Let \(h(x)=x-7\) and \(f(x)=x^{2}+2 .\) Find the following. $$h(0)$$

Short Answer

Expert verified
h(0) = -7

Step by step solution

01

Understand the given function

The function provided is h(x) = x - 7. Here, 'h' is a function of 'x' where each input value 'x' is decreased by 7.
02

Substitute x with 0

To find the value of h when x is 0, substitute x = 0 into the function. So, h(0) = 0 - 7.
03

Simplify the expression

Simplify the expression from Step 2. Therefore, h(0) = -7.

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Key Concepts

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

Function Substitution
Function substitution is a fundamental concept in algebra. It helps us determine the output of a function when the input is specified.
In our example, we have the function \(h(x) = x - 7\).
To find the value of \(h\) for a specific input, such as 0, we substitute this value into the function in place of \(x\).
This process of replacing \(x\) with another value is known as 'substitution'.
So, for \(h(0)\), we replace \(x\) with 0 to get \(h(0) = 0 - 7\).
In general, the goal of function substitution is to quickly and accurately find specific outputs for given inputs.
Evaluating Functions
Evaluating functions is the process of finding the value of a function for a particular input.
In our exercise, the function \(h(x) = x - 7\) is evaluated at \(x = 0\).
This involves directly applying the input value into the function.
For example:
  • First, identify the input value (in this case, 0).
  • Then, substitute this input into the function \(h(x)\).
  • We get \(h(0) = 0 - 7\).
  • Finally, we simplify the resulting expression.
This gives us the output value of the function for that specific input.
Simplifying Expressions
Simplifying expressions is the process of reducing a mathematical expression to its simplest form.
This makes it easier to understand and work with the expression.
In our example, after substituting \(x = 0\) in the function \(h(x) = x - 7\), we get the expression \(0 - 7\).
The next step is to perform the arithmetic operation:
  • Subtract 7 from 0, which gives us -7.
Therefore, \(h(0) = -7\).
Simplifying expressions helps ensure that we get correct and manageable results when evaluating functions.

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