Ans: C
Let $f(x)=k_1x + k_2x^2$, where $k_1$ and $k_2$ are non-zero constants. For $f(1)=5$, we have
Let $f(x)=k_1x + k_2x^2$, where $k_1$ and $k_2$ are non-zero constants. For $f(1)=5$, we have
$\begin{array}{rcl}
k_1(1) + k_2(1)^2 & = & 5 \\
k_1 + k_2 & = & 5 \ldots \unicode{x2460}
\end{array}$
For $f(2)=16$, we have
$\begin{array}{rcl}
k_1(2) + k_2(2)^2 & = & 16 \\
2k_1 + 4k_2 & = & 16 \\
k_1 + 2k_2 & = & 8 \ldots \unicode{x2461}
\end{array}$
$\unicode{x2461} – \unicode{x2460}$, we have
$\begin{array}{rcl}
k_2 & = & 3
\end{array}$
Sub. $k_2=3$ into $\unicode{x2460}$, we have
$\begin{array}{rcl}
k_1 + (3) & = & 5 \\
k_1 & = & 2
\end{array}$
Therefore, $f(x)=2x+3x^2$. Hence, we have
$\begin{array}{rcl}
f(3) & = & 2(3)+3(3)^2 \\
& = & 33
\end{array}$
