Question

a) the function $f(x) = \sqrt3{x}$, which has been stretched vertically by a factor of 5 and shifted to the left 2.
b) the function $f(x) = \sqrt{x}$, which has been reflected across the $y$-axis, stretched vertically by 2, and down 5.

Explanation:

Step1: Vertical stretch left shift

For $f(x)=\sqrt[3]{x}$, vertical stretch by 5 gives $5\sqrt[3]{x}$. Shift left 2: replace $x$ with $x+2$.
Expression: $y=5\sqrt[3]{x+2}$

Step2: Reflect y-axis, vert stretch, shift down

For $f(x)=\sqrt{x}$, reflect over y-axis: replace $x$ with $-x$ to get $\sqrt{-x}$. Vertical stretch by 2: $2\sqrt{-x}$. Shift down 5: subtract 5.
Expression: $y=2\sqrt{-x}-5$

Answer:

a) $y=5\sqrt[3]{x+2}$
b) $y=2\sqrt{-x}-5$