Question

Find the domain of the composite function fg.

f(x) = 2x + 10; g(x) =

Answer 1

f(x)=2x+10; g(x)=/[\sqrt{x}\]

Answer 2

\[\sqrt{x}\]

Answer 3

so u are looking for fog(x)? and the domain of that composite?

Answer 4

yes!

Answer 5

\[f(g(x))=2\sqrt{x}+10\]
for f(x) you know that this function can exist anywhere between (-infinity, infinity) because, if you remember when learning linear equations, you drew your lines (usually) with arrows point in both directions. That means that the line is extending infinitely in both directions.


For the case of sqrt(x), you may have learned that sqrt(-1) = i, an imaginary number. Since your domain is in the real number scale, you cannot have a negative number for x. What that means is that x must be equal to 0 or a positive number.


Since the domain of g(x) is smaller (because of the square root), then that is the more restrictive domain, which means it is the domain of the composite.

From this information, can you figure out what the domain of your composite function is?

Answer 6

i think its [\[[0,\infty)\]

Answer 7

that answer is correct

Answer 8

thank you!