/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 89 In Exercises 89-96, evaluate \(f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 89

In Exercises 89-96, evaluate \(f(4)\). \(f(x)=x^{2}\)

Short Answer

Expert verified
16

Step by step solution

01

Understand the function

The function given is \( f(x) = x^{2} \). This function takes a number \( x \) and squares it.
02

Substitute the value of x

We need to find \( f(4) \). Substitute \( x = 4 \) into the function: \( f(4) = 4^{2} \)
03

Calculate the square

Next, calculate the square of 4: \( 4^{2} = 16 \)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

quadratic functions
Quadratic functions are a type of polynomial function. They have the general form of







where \(a\), \(b\), and \(c\) are constants and \(x\) is the variable. In our case, the function is \(f(x) = x^2\). This means:
  • \(a = 1\)
  • \(b = 0\)
  • \(c = 0\)
Quadratic functions generally create a parabola, which is a symmetric curve on a graph. The given function \(f(x) = x^2\) represents the simplest form of a quadratic function. Here, every input value \(x\) is squared, making it always non-negative. This function graphically creates a parabola that opens upwards, with its vertex at the origin (0,0).
substitution
Substitution is a method used in algebra to replace a variable with a specific value. To find the value of a function at a particular point, we substitute the given number for the variable in the function: In our example, we need to evaluate \(f(4)\) for the function \(f(x) = x^2\).
  • First, identify the function: \(f(x) = x^2\).
  • Next, identify the point at which to evaluate the function: \(x = 4\).
  • Substitute the value of \(x = 4\) into the function: \(f(4) = 4^2\).
By substitution, we replace every occurrence of \(x\) with 4. This step is crucial because it simplifies our work to basic arithmetic operations, making it easier to solve the equation.
squaring a number
Squaring a number means multiplying that number by itself. It is represented mathematically as \(x^2\), which reads 'x squared'.
When you square a number, you essentially do:
  • \(4 \times 4\)
For instance, if you need to evaluate \(4^2\), it means you should multiply 4 by itself:
  • \(4^2 = 4 \times 4\)
  • This equals 16.
Squaring any positive or negative number always results in a non-negative value because a negative number times itself yields a positive result. For instance,
  • \((-3)^2 = (-3) \times (-3) = 9\)
The concept of squaring is foundational in algebra and appears frequently in various mathematical problems and functions.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the laws of exponents to compute the numbers. \(\left(2^{1 / 3} \cdot 3^{2 / 3}\right)^{3}\)

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\frac{1}{y x^{-5}}\)

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\left(\frac{3 x^{2}}{2 y}\right)^{3}\)

Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. \(\left(16 x^{8}\right)^{-3 / 4}\)

Compute the numbers. \(4^{-1 / 2}\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.