Answer:
The value of k if the graph of f passes through the point (3/4,0) is [tex]\mathbf{k=-\frac{9}{4}}[/tex]
Step-by-step explanation:
We are given the function: [tex]f(x)=\frac{k}{x}+3[/tex] where k is constant.
We need to find k, if the graph of f passes through the point (3/4,0).
So, graph passes through point (3/4,0) we have x=3/4 and y =0
Putting value of x in given function we can find value of x
We have f(x)=0, and x= 3/4
[tex]f(x)=\frac{k}{x}+3\\0=\frac{k}{\frac{3}{4} }+3[/tex]
Using fraction rule: [tex]\frac{a}{\frac{b}{c} }=\frac{a.c}{b}[/tex]
[tex]0=\frac{4k}{3 }+3\\Taking \ LCM\\0=\frac{4k+9}{3}\\3*0=4k+9\\0=4k+9\\4k=-9\\k=\frac{-9}{4}[/tex]
So, The value of k if the graph of f passes through the point (3/4,0) is [tex]\mathbf{k=-\frac{9}{4}}[/tex]
