Domain and Range of Composite Functions
Consider a function h(x)=x.
a) State the domain of h(x). {x|
}
b) State the range of h(x). {y|
}
Consider a composite function where f(x)=x2 and g(x)=√x.
f(g(x))=
f(g(x))=x but is the domain x∈R and the range y∈R?
a) Look at the diagram. State the domain of g(x). {x|
}
b) Look at the diagram. State the range of g(x). {y|
}
c) If these become the inputs for f(x), what is the range of (f∘g(x))? {y|
}
In summary, even though f(g(x))=x, the domain of f(g(x)) is {x|
}
and the range of f(g(x)) is {y|
}