Help with finding domain and range of a composite function with graph?

Question

anonymous · Answer

attachment

anonymous · Answer

can someone explain this second image.  My teacher solved it this way but i dont understand.  Would this be f(g(x)) or g(f(x))...i may have written it wrong.

jdoe0001 · Answer

hmmm    I don't get the 2nd image

but if you notice the 1st image....their domain and range overlap

so if the "piecewise function" is made from those 2 fuinctions    the domain would be the domain of $\bf f(x) \cup g(x)$

anonymous · Answer

does anyone get the image?

amistre64 · Answer

the second image is pretty messed up.

it starts out as if its defining g(f)  but then processes results for f(g)

the domain of g is adjusted fro -4,4 to -3.5,4 since that adjustment fits the range of g that is equal to domain elements of f

the adjusted domain of g is feed thru the function of g to produce an altered range for g;  adjusted from 0,4 to 0,3

this adjusted range of g is used as the input values for f, and as they feed thru f they produce the outputs from 0 to 2

there is no mathing going on, just mental adjustments.