Given two functions , f(x)=x^2+3 , where x is real , g(x)=|x|-5 , x is real , find gf(x).

i found gf(x)=x^2-2

is it true that the range of gf(x) is the same as the range of g(x) ? If so,

the range of g(x) is [-5 , infinity) and the range of gf(x) is [-2 , infinity)

why arent they the same ?