Question

Suppose that y varies directly with x, and y=3 when x=8

Answer 1

we are given

y varies directly with x

so, we can write equation as

$y=kx$

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

$3=k*8$

$k=\frac{3}{8}$

now, we can plug it back

$y=\frac{3}{8}x$

(A)

we have got equation as

$y=\frac{3}{8}x$

for finding inverse , we can switch x and y

$x=\frac{3}{8}y$

now, we can solve for y

$8*x=8*\frac{3}{8}y$

$8*x=3y$

$f^{-1}(x)=\frac{8x}{3}$............Answer

(B)

we have

$y=\frac{3}{8}x$

we can plug x=4 and find y

$y=\frac{3}{8}*4$

$y=\frac{3}{2}$................Answer