For $f(x)= x -3$ and $g(x)= x^ 2+4$ , how do you find f(g(x)) and g(f(x)) and state the range?

Question

1906 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-20T19:43:03

The answers are $f(g(x))=x^2+1$
and $g(f(x))=(x-3)^2+4$

This is a composition of functions

$f(x)=x-3$

$g(x)=x^2+4$

$f(g(x))=f(x^2+4)=x^2+4-3=x^2+1$

The range is $f(g(x)) in [1, +oo[$

$g(f(x))=g(x-3)=(x-3)^2+4$

The range is $g(f(x)) in [4, +oo[$

For f(x)= x -3f(x)= x -3 and g(x)= x^ 2+4g(x)= x^ 2+4, how do you find f(g(x)) and g(f(x)) and state the range?