2019 Nov P1 Q5

Question 5

Sketched below is the graph of $\,f(x)=k^x\,;\,k>0$ . The point $(4\; ;\,16)$ lies on $f$ .

$5.1$	Determine the value of $k$ .	$(2)$
$5.2$	Graph $g$ is obtained by reflecting graph $f$ about the line $y=x$ . Determine the equation of $g$ in the form $y=...$	$(2)$
$5.3$	Sketch the graph $g$ . Indicate on your graph the coordinates of two points on $g$ .	$(4)$
$5.4$	Use your graph to determine the value(s) of $x$ for which:
$\quad 5.4.1$	$f(x) \times g(x)>0$	$(2)$
$\quad 5.4.2$	$g(x) \leq -1$	$(2)$
$5.5$	If $h(x)=f(-x)$ , calculate the value of $x$ for which $f(x)-h(x)=\frac{\displaystyle 15}{\displaystyle 4}$	$(4)$
		$\textbf{[16]}$