f(x) = x^2 + 3 and g(x) = square root x-3

What is the domain of f(g(x))?

f(g(x))

I got f(g(x)) = x and thus the domain would be R, but this is not the answer.

f(g(x)) = x

Apparently I'm suppose to consider the domain of g(x) as-well? Could someone explain this please?

Asked Apr 24, 2014 by anonymous edited Apr 24, 2014 by Community

Like you say, f(g(x)) = (sqrt(x-3))^2 + 3 = x

However, it is only x if you can actually square root (x-3) in the first place. Otherwise there is nothing to square, etc etc. So while it generally simplifies to x, it is only valid when x≥3.

Answered Apr 24, 2014 by Collin Li (56,060 points) selected Apr 24, 2014 by Community

## Composite functions

Answered## 1 Answer