Chapter 5: Q 61. (page 298)

Graph each function and its inverse on the same Cartesian plane
$f (x) = {(\frac{1}{2})}^{x} f^{- 1} (x) = \log_{\frac{1}{2}} x$

Short Answer

Expert verified

The graph of the given expressions is :

Step by step solution

Step 1. Given information

Given expressions are

$f (x) = {(\frac{1}{2})}^{x} f^{- 1} (x) = \log_{\frac{1}{2}} x$

Step 2. Points of the Curve

Points of the function $f (x) = {(\frac{1}{2})}^{x}$

$x$	$f (x) = {(\frac{1}{2})}^{x}$
$1$	$0.5$
$0$	$1$
$- 1$	$2$

Step 3. Points of the Curve

Points of the function $f^{- 1} (x) = \log_{\frac{1}{2}} x$

x	$f^{- 1} (x) = \log_{\frac{1}{2}} x$
$4$	$- 2$
$1$	$0.5$
$0.25$	$2$

Step 4. Graph of the functions

The graph of the functions $f (x) = {(\frac{1}{2})}^{x}$ and $f^{- 1} (x) = \log_{\frac{1}{2}} x$ is as follows :

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Graph each function and its inverse on the same Cartesian plane
$f (x) = {(\frac{1}{2})}^{x} f^{- 1} (x) = \log_{\frac{1}{2}} x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Points of the Curve

Step 3. Points of the Curve

Step 4. Graph of the functions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Geometry

Logic and Functions

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function and its inverse on the same Cartesian planef(x)=(12)x f-1(x)=log12x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Points of the Curve

Step 3. Points of the Curve

Step 4. Graph of the functions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Geometry

Logic and Functions

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function and its inverse on the same Cartesian plane
$f (x) = {(\frac{1}{2})}^{x} f^{- 1} (x) = \log_{\frac{1}{2}} x$