Question

what is the domain of f[g(x)]?

Answer 1

1) Compute the value of g at x. This is g(x).

2) Compute the value of f at g(x). This is f(g(x)).

After all, this is technically exactly what function composition means. This is helpful because it tells you the conditions for a point x to be in the domain of f(g(x)). First, g must be defined at x. Second, f(g(x)) must be defined at g(x). Therefore, the domain of f(g(x)) is the intersection of the domain of g and the domain of the function obtained by symbolically substituting g(x) into f(x).

In your case, the domain of g is found as follows. Since g(x) = sqrt(2x + 4), the quantity 2x + 4 must be nonnegative:

2x + 4 >= 0,
2x >= -4,
x >= -2.

This is g's domain.

Now, assuming g is defined at a given x, symbolically substitute g(x) into f(x):

f(g(x)) = 2x + 4.

The domain of this expression is the set of values x such that f is defined at g(x). Clearly this domain is R.

The final domain is the intersection of { x in R : x >= -2 } and R, which is merely x >= -2.

The primary confusion over function composition is that the composition is NOT necessarily equivalent to the function represented by symbolically substituting g(x) into f(x) because the process of performing such a substitution assumes g is defined at x. Although the symbolic expression for the composite function will be the same as that obtained by substituting g(x) into f(x), the domains of the two symbolic expressions are not necesssarily equivalent, and thus the functions themselves are potentially different.

Yahoo answer : source

Answer 2

maybe you should check the questions before you copy-paste.....

Answer 3

No man I read and posted the yahhooo

Answer 4

Um... well I know that domain is x in coordinate points (x,y) but I'm not sure of this question. Like how to solve.

Answer 5

Read the Instructions @ChuckNora16

Answer 6

These are the choices they gave me. I'm assuming it's the third choice Lol. But I'm not sure.

Answer 7

I mean second choice. Not third.

Answer 8

The third one I suppose

Answer 9

LOLS

Answer 10

The second one says the domain of 'X'

Answer 11

did u get that

Answer 12

The domain of f(g(x)) is the domain of g(x) and the combined composite function f(g(x))

Answer 13

Well I'm not sure. That's why I'm asking for help. I knew what the second one said, but I guess it's wrong?

Answer 14

Yo