/*! 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 90 Is the function \(f\) defined by... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 90

Is the function \(f\) defined by \(f(x)=2^{x}\) for every real number \(x\) an even function, an odd function, or neither?

Short Answer

Expert verified
The function \(f(x) = 2^x\) is neither even nor odd because it does not satisfy the conditions \(f(x) = f(-x)\) for even functions and \(f(-x) = -f(x)\) for odd functions.

Step by step solution

01

Write down the given function

We are given the function \(f(x) = 2^x\) for every real number \(x\).
02

Calculate f(-x)

To check if the function is even or odd, we need to evaluate \(f(-x)\). \(f(-x) = 2^{-x}\)
03

Compare f(-x) to f(x) and -f(x)

Now, we compare \(f(-x)\) to \(f(x)\) and \(-f(x)\). - For even function, \(f(x) = f(-x)\). Check if there is any equivalence between the functions: \(f(x) = 2^x\) \(f(-x) = 2^{-x}\) As \(2^x\) is not equal to \(2^{-x}\), the function is not even. - For an odd function, \(f(-x) = -f(x)\). Check if there is any equivalence between the functions: \(-f(x) = -(2^x)\) \(f(-x) = 2^{-x}\) As \(- (2^x)\) is not equal to \(2^{-x}\), the function is not odd.
04

Determine if the function is even, odd, or neither

The function satisfies neither the conditions of even functions nor the conditions of odd functions. Therefore, the function is neither even nor odd.

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!

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

Suppose a television is playing softly at a sound level of 50 decibels. What decibel level would make the television sound eight times as loud?

Show that \((99+70 \sqrt{2})^{1 / 3}=3+2 \sqrt{2}\).

Explain why $$ 10^{100}\left(\sqrt{10^{200}+1}-10^{100}\right) $$ is approximately equal to \(\frac{1}{2}\).

Explain why every function \(f\) with exponential growth can be represented by a formula of the form \(f(x)=c \cdot 2^{k x}\) for appropriate choices of c and \(k\).

Show that if \(x\) and \(y\) are positive numbers, then $$ \sqrt{x+y}<\sqrt{x}+\sqrt{y}. $$ [In particular, if \(x\) and \(y\) are positive numbers, then \(\sqrt{x+y} \neq \sqrt{x}+\sqrt{y}\).]
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.