Answer:
D) (-1.6, -2.5)
Step-by-step explanation:
Please see attached for the graphing of the two functions.
The solution is the point where the two curves intersect.
From inspection of the graph, the solution is (-1.6, -2.5)
Proof
Given functions:
[tex]f(x)=\dfrac{4}{x}[/tex]
[tex]g(x)=\dfrac{9}{x-2}[/tex]
To find the solution:
[tex]\implies f(x)=g(x)[/tex]
[tex]\implies \dfrac{4}{x}=\dfrac{9}{x-2}[/tex]
Cross multiply:
[tex]\implies 4(x-2)=9x[/tex]
Expand:
[tex]\implies 4x-8=9x[/tex]
Simplify:
[tex]\implies -5x=8[/tex]
[tex]\implies x=-\dfrac{8}{5}=-1.6[/tex]
Inputting the found value of x into one of the equations and solving for y:
[tex]\implies f(-1.6)=\dfrac{4}{-1.6}=-2.5[/tex]
Therefore, the solution to f(x) = g(x) is (-1.6, -2.5) thus proving the graphed solution.
