Question

find the f-1(x) of f(x) =2x+1 over x-3

Answer 1

\[y= \frac{ 2x+1}{x-3}\]

Answer 2

swap x and y

Answer 3

\[x = \frac{2y +1}{y-3}\]

Answer 4

now

x(y-3) = 2y+1

xy -3x = 2y +1

Now get the y's together and factor

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

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

Answer 5

f ^(-1) (x) = (1+3x) / (x-2)