we are given
y varies directly with x
so, we can write equation as
[tex] y=kx [/tex]
where
k is a constant
now, we need to find k
we are given
y=3 when x=8
so, we can plug it and find k
[tex] 3=k*8 [/tex]
[tex] k=\frac{3}{8} [/tex]
now, we can plug it back
[tex] y=\frac{3}{8}x [/tex]
(A)
we have got equation as
[tex] y=\frac{3}{8}x [/tex]
for finding inverse , we can switch x and y
[tex] x=\frac{3}{8}y [/tex]
now, we can solve for y
[tex] 8*x=8*\frac{3}{8}y [/tex]
[tex] 8*x=3y [/tex]
[tex] f^{-1}(x)=\frac{8x}{3} [/tex]............Answer
(B)
we have
[tex] y=\frac{3}{8}x [/tex]
we can plug x=4 and find y
[tex] y=\frac{3}{8}*4 [/tex]
[tex] y=\frac{3}{2} [/tex]................Answer
