Chapter 1
Relationships





WeBWorK1.5 The Algebra of Functions

Exercises

Flash & Math grapherFor each of the following functions,

    1. graph the function,
    2. graph the inverse relation, and
    3. decide whether the inverse is a function.

(Note: The graphing calculator provided here requires `x` as the independent variable. Adjust your function definitions as necessary.)

1.   `ftext[(]x text[)]=x^3`     2.  `gtext[(]x text[)]=1/(x^2)`
3.  `htext[(]x text[)]=-1/2  x+3`     4.  `ftext[(]t text[)]=3/(t+5)`
5.   `gtext[(]t text[)]=3/(t^2+5)`     6.   `htext[(]t text[)]=(3 t)/(t+5)`
7.   `Ftext[(]x text[)]=2^x`   8.   `Gtext[(]x text[)]=sqrt(1+x)`
9.   `Htext[(]x text[)]=sqrt(1+x^2)`   10.   `Ftext[(]t text[)]=log_10text[(]t text[)]`
11.   `Gtext[(]t text[)]=sqrt(t-1)`     12.   `Htext[(]t text[)]=sqrt(1-t^2)`

For each of the following functions,

    1. state the domain of the function, and
    2. if the inverse relation is a function, state its domain as well.
13.   `ftext[(]x text[)]=x^3`     14.  `gtext[(]x text[)]=1/(x^2)`
15.  `htext[(]x text[)]=-1/2  x+3`     16.  `ftext[(]t text[)]=3/(t+5)`
17.   `gtext[(]t text[)]=3/(t^2+5)`     18.   `htext[(]t text[)]=(3 t)/(t+5)`
19.   `Ftext[(]x text[)]=2^x`   20.   `Gtext[(]x text[)]=sqrt(1+x)`
21.   `Htext[(]x text[)]=sqrt(1+x^2)`   22.   `Ftext[(]t text[)]=log_10text[(]t text[)]`
23.   `Gtext[(]t text[)]=sqrt(t-1)`     24.   `Htext[(]t text[)]=sqrt(1-t^2)`

  1. If f ( x ) = x 2 / 3 + 3 for x ≥ 0 , find a formula for f - 1 .

  2. If f ( x ) = x 2 / 3 + 3 for x ≥ 0 , make a table of values for f - 1 with at least five entries.

  3. For any given base `b`, there are two pairs of numbers `x` and `y` that we can easily see will satisfy

    `y=log_bx`   if and only if   `x=b^y`.

    One pair is `x=1` and `y=0`. What's the other?

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