Find f(g(x))...help please?

Question

Given f(x)=3x+5 and g(x)=sqrt(x-1), find f(g(x)) and the domain of f(g(x)).

I know that this becomes 3(sqrt[x-1])+5, but I'm not sure what to do with it after this. Can someone help me please?

Answer 1

once you distribute can't go any further, the domain is [-1,infinity)

Answer 2

The domain is the set of all possible values for x. Since you have sqrt(x-1), x must be greater than or equal to 1.

Answer 3

Your answer is correct.

The domain is x-1>0 or x>1

{x|x>1} ANSWER

Answer 4

f(g(x)) = 3(sqrt(x-1)) + 5, as you say

the domain is all of the values you can use in place of x.

Since the root is taken of (x-1), x-1 >= 0 so x >= 1 is the domain. The range is what will come out of it which will be 5 to infinity.