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Chapter 3: Problem 62

Let \(h(x)=x-7\) and \(f(x)=x^{2}+2 .\) Find the following. $$f(-10)$$

Short Answer

Expert verified
102

Step by step solution

01

Understand the function

The function to be evaluated is given by: \[f(x) = x^2 + 2\]We need to find the value of this function when \(x = -10\).
02

Substitute -10 into the function

Replace the variable \(x\) with \(-10\) in the function: \[f(-10) = (-10)^2 + 2\]
03

Calculate the square term

First, calculate the square of \(-10\): \[(-10)^2 = 100\]
04

Add 2 to the squared value

Now add 2 to the result of the square: \[f(-10) = 100 + 2\]
05

Find the final result

Add the numbers to get the final result: \[f(-10) = 102\]

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Key Concepts

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

Substitution
In algebra, substitutions help us simplify and evaluate functions and expressions. When given a variable, like in the function \(f(x) = x^2 + 2\), you can substitute a specific number for that variable to find the value of the function at that point.
For instance, in the exercise, we need to find \(f(-10)\). Here鈥檚 how substitution works step-by-step:
  • Identify the function and the value to substitute.
  • Replace every instance of the variable with the provided value.
  • Simplify the resulting expression to find the answer.
By following these steps, we replaced \[x\] with \[-10\] in the function \(x^2 + 2\), making it \( (-10)^2 + 2 \)
Squaring a Number
Squaring a number means multiplying the number by itself. For example, squaring \(-10\)\
Basic Algebra Steps
Basic algebra steps involve operations like addition, subtraction, multiplication, and division. These steps are essential for evaluating and simplifying functions.
In our exercise, after substituting and squaring, the following basic algebra steps were used:
  • Addition

After computing \((-10)^2 = 100\), the next step is to add 2 to the result:
\100 + 2 = 102\.

This final step combines all the values we have calculated to find the function's output at \(-10\).

Basic algebra steps allow us to manipulate numbers and expressions to find solutions efficiently.

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Most popular questions from this chapter

Students in a Listening Responses class bought 40 tickets for a piano concert. The number of tickets purchased for seats in either the first mezzanine or the main floor was the same as the number purchased for seats in the second mezzanine. First mezzanine seats cost 52 dollars each, main floor seats cost 38 dollars each, and second mezzanine seats cost 28 dollars each. The total cost of the tickets was 1432 dollars. How many of each type of ticket were purchased?

Making Change. Monica buys a $$ 9.25\( book using a $$ 20\) bill. The store has no bills and gives change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?

Exercise. Huan jogs and walks to school each day. She averages \(4 \mathrm{km} / \mathrm{h}\) walking and \(8 \mathrm{km} / \mathrm{h}\) jogging. From home to school is \(6 \mathrm{km}\) and Huan makes the trip in 1 hr. How far does she jog in a trip?

The perimeter of a rectangular oceanfront lot is \(190 \mathrm{m}\). The width is one-fourth of the length. Find the dimensions.

$$ \begin{aligned} y+z &=1 \\ x+y+z &=1 \\ x+2 y+2 z &=2 \end{aligned} $$
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