If the range is all real numbers, for which x do we have g(f(x)) = -1? Be sure to calculate g(f(x)) by applying f to x and then g to the result, not 4 - x to x. Concerning "gof(x)=4-x", recall that a function includes not just a way to convert an input into an output, but also a domain. The fact that two functions are equal implies that their domains are the same.f(x)=sqrt(4-x)

g(x)=x^2

Find the range of gof:

gof(x)=4-x

Shouldn't the range be all real numbers? Because it is a linear function. But the answer key says [0,infinity[ ??

If the range is [0,infinity[, for which x do we have f(g(x)) = 0? Again, forget fog(x)=x^2 and calculate f(g(x)) by definition for the specific x that you think should work.Given two functions:

f(x)=1/x (x cannot be 0)

g(x)1/x^2 (x cannot be 0)

Find the range of fog

fog(x)=x^2

Shouldn't the range by [0,infinity[ ?? The answer key says ]0,infinity[