Question

Compare the domains of the logarithmic function f(x) and the square root function g(x).

Answer 1

Answer:

The domain of the function $g(x)$ is greater than the domain of the function $f(x).$

Step-by-step explanation:

The diagram shows the logarithmic function $f(x)$. The domain of this function is

$x>-3$

The domain of the square root function $g(x)=\sqrt{x+3}+1$ is

$x+3\ge 0\\ \\x\ge -3$

The domain of the function $g(x)$ is greater than the domain of the function $f(x),$ because the set $x\ge -3$ contains the set $x>-3$ ( $(-3,\infty)\subset [-3,\infty)$).