Determine the roots of f(x) = -x2 - 2x2 + 5x + 6.

The final answer is:

2.1.2 State whether $f(x)$ is a function or a non-function.

The x-values in $f(x)$ are $-2, 0, 1, 2$. Each x-value is unique and corresponds to only one y-value.
The final answer is:

2.2
The figure below represents the graph of $g(x): y = a^x$ with domain $x \in \mathbb{R}$. Point A lies on $g(x)$ and the co-ordinates of A are $(4; 8)$.

2.2.1 Determine the equation for $g(x)$ and leave the answer in the form $y = ...$

The final answer is:

2.2.2 Determine the equation of $g^{-1}(x)$. Give the answer in the form $x = ...$

$y = 2^{\frac{3x}{4}}$.

This equation is already in the requested form $x = ...$.
The final answer is:

2.2.3 Write down an equation for the asymptote of $g^{-1}(x)$.

Exponential functions of the form $y = b^x$ have a horizontal asymptote at $y=0$.

The asymptote of an inverse function is found by swapping the variables in the asymptote of the original function.
If the asymptote for $g(x)$ is $y=0$, then the asymptote for $g^{-1}(x)$ is $x=0$.
The final answer is: