Range of Composite Function

= x2+ x+ for x
= x2+ x+ for x
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1st graph: 2nd graph:


Summary

The function gf is defined only if Rf ⊆ Dg.
The function fg is defined only if Rg ⊆ Df.
Domain of gf = domain of f.
Domain of fg = domain of g.
To find range of gf, apply the range of f as domain on the graph of g.
To find range of fg, apply the range of g as domain on the graph of f.