Domain & Range of a Function
Exercises for students
Solve the following problems on paper and check your answers using the above applet:
The function f is defined by
f(x) = x + 3/2 for -3 < x <= -1
f(x) = -(x^3)/2 for -1 < x <= 2
f(x) = x - 6 for 2 < x <= 4
Sketch the graph of f and state the range of f.
The functions f and g are defined by f(x) = ln (1 + x) and g(x) = 1 - exp(-x), where in each case the domain is R+.
Find the range of the composite function gf.
The functions f and g are defined by f(x) = ln (1 + x) and g(x) = x^2 + 2x, where in each case the domain is { x : x real, x > -1 }.
Find the ranges of f and g.
Give the rule for the composite function fg, and state its range.
You can define the functions using the following operators:
| + | - | * | / | ^ |
| abs( ) | sqrt( ) | ln( ) | exp( ) | pi |
| sin( ) | cos( ) | tan( ) |
| asin( ) | acos( ) | atan( ) |
| sinh( ) | cosh( ) | tanh( ) |
Right-click here to download this page, the Java Class File and unzip the Javathings Math Package.
This applet uses the com.javathings.math package developed by:
Patrik Lundin
patrik@javathings.com
http://www.javathings.com