Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

6.2: Operations on functions given by tables

( \newcommand{\kernel}{\mathrm{null}\,}\)

We can also combine functions that are defined using tables.

Example 6.2.1

Let f and g be the functions defined by the following table.

x1234567f(x)6314076g(x)4025231

Describe the following functions via a table:

  1. 2f(x)+3
  2. f(x)g(x)
  3. f(x+2)
  4. g(x)

Solution

For (a) and (b), we obtain by immediate calculation

x12345672f(x)+315951131715f(x)g(x)2311245

For example, for x=3, we obtain 2f(x)+3=2f(3)+3=21+3=5 and f(x)g(x)=f(3)g(3)=12=1.

For part (c), we have a similar calculation of f(x+2). For example, for x=1, we get f(1+2)=f(1+2)=f(3)=1.

x123456710f(x+2)14076 undef.  undef. 63

Note that for the last two inputs x=6 and x=7 the expression f(x+2) is undefined, since, for example for x=6, it is f(x+2)=f(6+2)=f(8) which is undefined. However, for x=1, we obtain f(x+2)=f(1+2)=f(1)=6. If we define h(x)=f(x+2), then the domain of h is therefore Dh={1,0,1,2,3,4,5}.

Finally, for part (d), we need to take x as inputs, for which g(x) is defined via the table for g. We obtain the following answer.

x1234567g(x)4025231

Example 6.2.2

Let f and g be the functions defined by the following table.

x1357911f(x)3511497g(x)7691195

Describe the following functions via a table:

  1. fg
  2. gf
  3. ff
  4. gg

Solution

The compositions are calculated by repeated evaluation. For example,

(fg)(1)=f(g(1))=f(7)=4

The complete answer is displayed below.

x1357911(fg)(x)4 undef. 97911(gf)(x)695 undef. 911(ff)(x)5117 undef. 94(gg)(x)11 undef. 9599


This page titled 6.2: Operations on functions given by tables is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform.

Support Center

How can we help?