Question 455322: What does it mean to "find the domain and range of the composition f of g? and to write the answer in "set notation" ??? Thank you
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What does it mean to "find the domain and range of the composition f of g? and to write the answer in "set notation" ???
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A function is a machine. You feed it "x" and
it gives you f(x).
Now, if you feed f(x) to another machine, g,
you will get g[f(x)]
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That is what composition is. It's two machines
operating one after another.
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Example:
f(x) = x+3
g(x) = 2x
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fog(x) = f[g(x)] = f[2x] = 2x+3
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OR
gof(x) = g[f(x)] = g[x+3] = 2(x+3) = 2x+6
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If an answer happens to be x = 2, or x = 3
the set notation would look like {x | x = 2 or x = 3}
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Cheers,
Stan H.
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