Question

Find the domain of the composite function F(f(x)).
F(x)= x+3, g(y)=4/ sqr root of y
G(f(x))= 4/ sqr root of x+3

Answer 1

when the function is under a square root, the function's domain is everywhere that makes the function non-negative, also since there is a fraction you cannot have a zero in the denominator

Answer 2

Denominator cannot be 0. For what value of x does sqrt(x+3) = 0?

Answer 3

oops right. The expression in the radical sign x+3 must be greater than zero. AND it cannot equal zero. So domain is x+3\[\ge\]0. Solve that inequality for x.

Answer 4

Oops again I mean >

Answer 5

so looking at this closely, sqrt(x+3) you are look for an x that doesnt result in a negative so x must be greater than or equal to -3, but it is also under a fraction so when it is equal to -3 it becomes zero and we do not want that in the denominator so its everywhere greater than -3 but not equal to 3 or in other words\[(-3,\infty)\]

Answer 6

i mean -3 on that last line not 3