Q.89 (a) Graph f(x)=3x+1聽and g(x)=2x... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q.89 (page 316)

(a) Graph $f (x) = 3^{x + 1}$ and $g (x) = 2^{x + 2}$ , on the same Cartesian plane.
(b) Find the points of intersection of the graphs of f and g by solving $f (x) = g (x)$ Round answers to three decimal places. Label any intersection points on the graph drawn in part (a).
(c) Based on the graph, solve $f (x) > g (x)$ .

Short Answer

Expert verified

a) The graph can be given as

b) The point of intersection is $(0.71.6.541)$

c) $f (x) > g (x)$ when $x > 0.71$

Step by step solution

Given information

We are given

$f (x) = 3^{x + 1} g (x) = 2^{x + 2}$

Part a) Step 2: Graph f(x)

We use a table to graph the function

$x$	$f (x) = 3^{x + 1}$
-2	$\frac{1}{3}$
$- 1$	$1$
$0$	$3$
$1$	$9$
$2$	27

Similarly table for $g (x) = 2^{x + 2}$ can be given as

x	$g (x) = 2^{x + 2}$
-2	1
-1	2
0	4
1	8
2	16

Part a) Step 2: Graph the functions

The graph can be given as

Part b) Step 1: Solve for f(x)=g(x)

We get,

$f (x) = g (x) 3^{x + 1} = 2^{x + 2} \ln (3^{x + 1}) = \ln (2^{x + 2}) (x + 1) \ln 3 = (x + 2) \ln 2 x (\ln 3) + \ln 3 = x (\ln 2) + 2 (\ln 2) x (\ln 3) - x (\ln 2) = 2 (\ln 2) - \ln 3 x = \frac{2 (\ln 2) - \ln 3}{(\ln 3) - (\ln 2)} x = \frac{\ln (\frac{4}{3})}{\ln \frac{3}{2}} x = 0.71$

Now we find the corresponding function value

$f (x) = 3^{x + 1} f (0.71) = 3^{0.71 + 1} f (0.71) = 6.541$

Hence the point of intersection is $(0.71, 6.541)$

Part c) Step1: Solve f(x)>g(x)

From part b) We know that the two graphs intersect at $(0.71, 6.541)$ and from the graph we can conclude that $f (x) > g (x)$ for $x > 0.71$

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91影视

Short Answer

Step by step solution

Given information

Part a) Step 2: Graph f(x)

Part a) Step 2: Graph the functions

Part b) Step 1: Solve for f(x)=g(x)

Part c) Step1: Solve f(x)>g(x)

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91影视

(a) Graph f(x)=3x+1and g(x)=2x+2, on the same Cartesian plane.(b) Find the points of intersection of the graphs of f and g by solving f(x)=g(x)Round answers to three decimal places. Label any intersection points on the graph drawn in part (a).(c) Based on the graph, solve f(x)>g(x).

Short Answer

Step by step solution

Given information

Part a) Step 2: Graph f(x)

Part a) Step 2: Graph the functions

Part b) Step 1: Solve for f(x)=g(x)

Part c) Step1: Solve f(x)>g(x)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Statistics

Mechanics Maths

Pure Maths

Calculus

Study anywhere. Anytime. Across all devices.