Chapter 5: Q.96 (page 316)

(a) Graph $g (x) = 3^{x} - 9$ g
(b) Find the zero of g.
(c) Based on the graph, solve $g (x) < 0$

Short Answer

Expert verified

a) The graph of the function is

b) The zero of the function is $x = 2$

c) $g (x) < 0$ when $x < 2$

Step by step solution

Step !: Given information

We are given a function $g (x) = 3^{x} - 9$

We create a table

We get

x	$g (x) = 3^{x} - 9$
-1	$- \frac{28}{3}$
0	-8
1	-6
2	0
3	18

The graph of the function can be given as

Part b) Step 2: Solve for g(x)=0

We get,

$g (x) = 0 3^{x} - 9 = 0 3^{x} = 9 3^{x} = 3^{2} x = 2$

The zero of the function is at $x = 2$

Part c) Step 1: Solve for g(x)<0

As the zero of the function is at x=2

Hence $g (x) < 0$ when $x < 2$

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(a) Graph $g (x) = 3^{x} - 9$ g
(b) Find the zero of g.
(c) Based on the graph, solve $g (x) < 0$

Short Answer

Step by step solution

Step !: Given information

We create a table

Part b) Step 2: Solve for g(x)=0

Part c) Step 1: Solve for g(x)<0

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(a) Graphg(x)=3x-9 g(b) Find the zero of g.(c) Based on the graph, solveg(x)<0

Short Answer

Step by step solution

Step !: Given information

We create a table

Part b) Step 2: Solve for g(x)=0

Part c) Step 1: Solve for g(x)<0

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

(a) Graph $g (x) = 3^{x} - 9$ g
(b) Find the zero of g.
(c) Based on the graph, solve $g (x) < 0$