Posted by **CheezyReezy** on Friday, June 3, 2011 at 1:46am.

Find the domain of the composite function f ₒ g . Please show all of your work.

f(x) = √x; g(x) = 2x + 12

- Math - Domain of Composite function -
**Jai**, Friday, June 3, 2011 at 6:06am
f(x) = sqrt(x)

g(x) = 2x + 12

thus,

(fog)(x) = sqrt(2x + 12)

note that to get the domain, you must get the intersection of the 3 function domains.

for f(x) = sqrt(x), x cannot be less than zero thus the domain is [0 , +infinity)

for g(x) = 2x + 12, x can be any real number thus domain is (-infinity, +infinity).

for (fog)(x) = sqrt(2x + 12), the lowest possible value of the radicand (term inside the radical sign) is zero. thus equating 2x + 12 to zero,

2x + 12 = 0

x = -6

thus domain is [-6 , +infinity)

the intersection of the three domains is therefore,

[0, +infinity)

hope this helps~ :)

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