Question

over the set of real numbers, what is the domain of the composite function g(f(x))?
f(x)=3-x,g(y)=square root of y
g(f(x))=square root of 3-x

Answer 1

hey i got \[x \le3 \]

Answer 2

\( g(y) = \sqrt{y} \)

\(f(x) = 3 - x\)

\(g(f(x)) = g(3 - x)\)

\(g(f(x)) = \sqrt{3 - x} \)

The domain is the set of values that will make the radicand non-negative:

\(3 - x \ge 0\)

\(-x \ge -3\)

\(x \le 3 \)

You are correct.

Answer 3

thanks

Answer 4

wlcm