CompositionA3. The composition (or composite) of f with g, written as f (g (x)) and read as
“f of g of x,” is the function obtained by replacing x wherever it occurs in f(x) by
g(x). We also write (f g) (x) for f(g(x)). The domain of (f g) (x) is the set of all
x in the domain of g for which g(x) is in the domain of f.
Example 4A __
If f(x) = 2x − 1 and g(x) = x^2 , then does f (g (x)) = g (f (x))?
SOLUTION: f (g (x)) = 2 (x^2 ) − 1 = 2x^2 − 1
g (f (x)) = (2x − 1)^2 = 4x^2 − 4x + 1.In general, f(g(x)) ≠ g(f(x)).
Example 4B __
If f(x) = 4x^2 − 1 and g(x) = , find f (g(x)) and g(f(x)).
SOLUTIONS:.
SymmetryA4. A function f is if, for all x in the domain of .The graph of an odd function is symmetric about the origin; the graph of an even
function is symmetric about the y-axis.