Question 140634
f(x) = 2x-5 divided by x+4, find f-1(x).
:
f(x) = y
:
y = {{{(2x-5)/(x+4)}}}
solve for x:
Multiply both sides by (x+4)
2x - 5 = y(x+4)
2x - 5 = xy + 4y
2x = xy + 4y + 5
2x - xy = 4y + 5
x(2-y) = 4y + 5
x = {{{(4y+5)/(2-y)}}}


:
To find the inverse, swap x and y:
y = {{{(4x+5)/(2-x)}}}
f-1(x) = {{{(4x+5)/(2-x)}}}