Let $f(x)=\sqrt{x}$. Find $g(x)$, the function that is $f(x)$ reflected over the $x$-axis and horizontally stretched by a factor of 3 . \[ g(x)= \] help (formulas) Submit answer

Step 1 ：Let $f(x)=\sqrt{x}$

Step 2 ：Find $g(x)$, the function that is $f(x)$ reflected over the $x$-axis and horizontally stretched by a factor of 3

Step 3 ：The reflection of a function over the x-axis is achieved by taking the negative of the function

Step 4 ：The horizontal stretch by a factor of 3 is achieved by replacing x with x/3 in the function

Step 5 ：Apply these transformations to the function $f(x) = \sqrt{x}$

Step 6 ：So, $g(x) = -\sqrt{x/3}$

Step 7 ：Simplify the final answer

Step 8 ：\(\boxed{g(x) = -\frac{\sqrt{3}}{3}\sqrt{x}}\)