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?

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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[#