Composite Functions


Exercises for students
Solve the following problems on paper and check your working using the above applet:

Let f(x) = x² + 3x + 1, 0 < x < 1
Let g(x) = -x² + 4x + 2, 1 < x < 7
Is the composite function gf defined?
If yes, give its rule, domain and range.
If no, give a reason why.

Let f(x) = x² + 3x + 1, 0 <= x < 1
Let g(x) = -x² + 4x + 2, 1 < x < 7
Is the composite function gf defined?
If yes, give its rule, domain and range.
If no, give a reason why.

Let f(x) = x² + 3x + 1, -2 < x < 1
Let h(x) = -x² + 4x + 2, -2 < x < 7
Is the composite function hf defined?
If yes, give its rule, domain and range.
If no, give a reason why.

Summary

The function gf is defined only if R_f is a subset of D_g
The function fg is defined only if R_g is a subset of D_f
D_gf = D_f
D_fg = D_g
R_gf can be found from the graph of g by restricting the domain to R_f
R_fg can be found from the graph of f by restricting the domain to R_g



Right-click here to download this page and the Java Class File.