6.1 Given: $g(x) = 3^x$ 6.1.1 Write down the equation of $g^{-1}$ in the form $y = ...$ 6.1.2 Point $P(6 ; 11)$ lies on $h(x) = 3^{x - 4} + 2$ - NSC Mathematics - Question 6 - 2021 - Paper 1

The point $P(6 ; 11)$ can be transformed to find the corresponding coordinates on the graph of $g$.
First, we calculate the translation:

• Move 4 units left: New x-coordinate $= 6 - 4 = 2$.
• Then add 2: New y-coordinate $= 11 - 2 = 9$.
  Thus, the coordinates of the image of $P$ on $g$ are $(2, 9)$.

We know that the asymptote of the function $f(x) = 2^{p}*x + q$ is $y = -16$. This asymptote indicates the value of $q$. Therefore, we have:
$q = -16$.
To find $p$, substitute the point $T(3 ; 16)$ into the function:
$16 = 2^{p}*3 + q$
Substituting for $q$:
$16 = 2^{p}*3 - 16$
Now, rearranging gives:
$32 = 2^{p}*3$
Thus,
2^{p} = rac{32}{3}
To find $p$, we can convert $32$ to a power of $2$:
$32 = 2^5$
This implies:
$2^{p} = 2^{5 - ext{log}_2(3)}$
Therefore,
$p ext{ is approximately } 5 - ext{log}_2(3) ext{ or } p = 2$.