How do I find out the domain of a composite function Watch

JacobBob
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if fgx is the function, and I am given the domains of both fx and gx
To determine the domain of fgx, should I find the domain of the new composite function and gx and then take the overlap between both ?
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RDKGames
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(Original post by JacobBob)
if fgx is the function, and I am given the domains of both fx and gx
To determine the domain of fgx, should I find the domain of the new composite function and gx and then take the overlap between both ?
You should determine for which set of values of x we have g coinciding with the domain of f.

Then take the intersection between this set and the domain of g. The result is the domain of fg.

Example: Let f(x) = \sqrt{x} for x \geq 4 and g(x) = 2x for x < 3.

For domain of fg(x), we first solve g(x) \geq 4. This yields x \geq 2. The intersection between the set \{ x \geq 2 \} and \{ x < 3 \} is 2 \leq x < 3. Hence this is the domain of fg(x) = \sqrt{2x}.
Last edited by RDKGames; 3 weeks ago
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