Mathematics for IGCSE & O level - Functions (Section 1 - No. 27)
Which of the following is true regarding composite functions g(f(x))?
The result of g(f(x)) is found by substituting f(x) into g(x).
The domain of g(f(x)) is limited by the range of f(x).
If f(x) = x+1 and g(x) = 2x, then g(f(x)) = 2x+1.
The domain of g(f(x)) is limited by the domain of f(x).
Explication
g(f(x)) means substituting f(x) into g(x), and the domain of g(f(x)) is limited by the domain of f(x). And the range of f(x) determines the domain of g(x).