How to determine domain and range for composite function wor? still blur
vick5821 发表于 11-10-2010 04:35 PM
如果他是问valid ....
f(x)=x^2 -1
g(x)= x^(1/2)
h(x) = 1/x
let A(x) = g.f(x) <<<< range of f(x) must be subset of domain g(x)
range of f(x) is f(x)>= -1
domain of g(x) is x>=0
so to make g.f(x) valid , x must more or equal to 1 so that range of f(x) >=0
so , domain of A(x) is x >=1 , and range is A(x)>=0
F(x) = h。A(x) <<<range of A(x) must be subset of domain h(x)
range A(x)>=0
domain of h(x) = x can be any real number but not equal to 0 ,
so to make F(x) valid , x must more than 1 so that range of A(x) >0
so , domain of F(x) is x> 1 and range of F(x) > 0