Graph of Composite & Inverse Functions
Exercises for students
Solve the following problems on paper and check your graphs using the above applet:
Functions f and g are defined by f(x) = x^2, x real and g(x) = sqrt(x), x>0.
Sketch on separate, clearly labelled diagrams the graphs of y = f(x), y = g(x), y = gf(x), y = fg(x).
Functions f and g are defined by f(x) = exp(x), x real and g(x) = x - 1, x real.
Sketch in a single diagram the graphs of y = f(x), y = g(x), y = gf(x), y = fg(x), labelling each graph clearly.
State briefly the relationship
(i) between the graphs of f and gf
(ii) between the graphs of f and fg
The function f is defined by f(x) = 4(x^3) + 3, x real.
State a relationship between the graphs of f and f -1.
Summary
The composite function gf is defined only if Rf is a subset of Dg.
The composite function fg is defined only if Rg is a subset of Df.
Dgf = Df
Dfg = Dg
Use Rf and the graph of g to find Rgf
Use Rg and the graph of f to find Rfg
The inverse function f -1 is defined only if f is a one-one function.
The inverse function g -1 is defined only if g is a one-one function.
Df -1 = Rf
Rf -1 = Df
You can define the function 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