Question

Let f(x)=x+3 and g(x)=(-)sqrt x
find g(f(x))
what is the domain of g(f(x))?

Answer 1

x>-3

Answer 2

can you please explain the steps to me?

Answer 3

sqrt is not defind (at least in R) for negative numbers. So x+3 have to be > 0

Answer 4

to find g(f(x)) just put the expression of f(x) in the place of (x) in the expression of g(x0

g(f(x)) = -sqrt f(x) = -sqrt(x+3)

square root is not defined for negative numbers
so
x+3 ≥0
x≥-3

Answer 5

hoblos i sright x>=-3

Answer 6

thank you so much!

Answer 7

how about this one?\[\sqrt{(9x^3+54x^2+81x)} /(x^3-4x^2+4x\]