Let $f : \mathbb{R}^2 \to \mathbb{R}$ be defined by $f(x,y) = 3x^{4}+6y^{5}+3$ and set $z = f(x,y)$.

(a) The level sets of $f$ are subsets of $\mathbb{R}^k$ for $k =$ .

(b) Find an equation for the level set of $f$ at level $z = 1$. This level set is the set of all points $(x,y)$ in $\mathbb{R}^2$ that satisfy the equation

. help (equations)