Question

Find the inverses

1)
y=9/x
x=9/y
xy=9
y=9/x Which is wrong I believe

2)
y=(2x+1)/(3-2x) How do I get rid of the ys after I replace the xs with them?

Answer 1

f^-1(9/x) = 9/x
since

f^-1(f(x)) = 9/(f(x)) = 9/(9/x) = x

swap variables and solve for y:

x = (2y+1)/(3-2y)
x(3-2y) = 2y+1
3x-2xy = 2y+1
3x-1 = 2xy+2y
3x-1 = y(2x+2)
y = (3x-1)/(2x+2)