/*! 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} Q. 46 Suppose that f(x)=log2(x-2)+1.(a... [FREE SOLUTION] | 91影视

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Chapter 5: Q. 46 (page 349)

Suppose that f(x)=log2(x-2)+1.

(a) Graph f.

(b) What is f(6)? What point is on the graph of f ?

(c) Solve f(x)=4. What point is on the graph of f ?

(d) Based on the graph drawn in part (a), solve f(x)>0.

(e) Find f-1(x). Graphf-1 on the same Cartesian plane as f.

Short Answer

Expert verified

Part (a) Graph of fand f-1:

Part (b) f(6)=3;point on the graph: (6,3)

Part (c) f(10)=4;point on the graph: (10,4)

Part (d) 52,鈭�

Part (e)f-1(x)=2x-1+2

Step by step solution

01

Part (a) Step 1. Given information  

A function,f(x)=log2(x-2)+1

02

Part (a) Step 2. Graph of the function

Graph of the function is:

03

Part (b) Step 1. Finding f(6), and point on the the graph it represents

Given, f(x)=log2(x-2)+1

f(6)=log2(6-2)+1

f(6)=log24+1

f(6)=2+1

f(6)=3

The point on the graph is: (6,3)

04

Part (c) Step 1. Solving f(x)=4, and finding point on the graph it represents

Given, f(x)=4

log2(x-2)+1=4

log2(x-2)=4-1

x-2=23

x=8+2

x=10

The point on the graph is:(10,4)

05

Part (d) Step 1. Solving f(x)>0

Given, f(x)>0

鈬�log2(x-2)+1>0

鈬�log2(x-2)>-1

鈬�x-2>2-1

鈬�x>2+12

鈬�x>52

06

Part (e) Step 1. finding and graphing f-1(x)

In the function, replace x by f-1(x)and f(x)by x and rearrange the variables to get inverse of the function.

x=log2(f-1(x)-2)+1

鈬�x-1=log2(f-1(x)-2)

鈬�2x-1=f-1(x)-2

鈬�f-1(x)=2x-1+2

Graph of f-1:

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