Chapter 2.2, Problem 8E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# In Exercises 1-12, compute the missing values in the following table, and supply a valid technology formula for the given function: [HINT: See Quick Examples 1-4.] x –3 –2 –1 0 1 2 3 f ( x ) h ( x ) = − 2 ( 3 − x )

To determine

To calculate: The unknown values of table for the function h(x)=2(3x) also determine the technology formula for the function, table is shown below:

 x −3 −2 −1 0 1 2 3 h(x)
Explanation

Given Information:

The function is h(x)=ā2(3āx).

The provided table is,

 x ā3 ā2 ā1 0 1 2 3 h(x)

Formula used:

Inverse of an exponential function for any x and b is given by:

bāx=1bx

Calculation:

Consider the provided function,

h(x)=ā2(3āx)

Substitute x=ā3 in h(x)=ā2(3āx):

h(ā3)=ā2(3ā(ā3))=ā2(33)=ā54

Substitute x=ā2 in h(x)=ā2(3āx):

h(ā2)=ā2(3ā(ā2))=ā2(32)=ā18

Substitute x=ā1 in h(x)=ā2(3āx):

h(ā1)=ā2(3ā(ā1))=ā2(31)=ā6

Substitute x=0 in h(x)=ā2(3āx):

h(0)=ā2(30)=ā2

Substitute x=1 in h(x)=ā2(3āx):

h(1)=ā2(3ā1)

Use the formula bāx=1bx to solve further,

f(1)=ā2(3ā1)=ā231

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