How do you find the inverse function of #f(x) = (2x-3)/(x+4)#?

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Answer 1 · 2015-06-12T17:38:00

You can swap #x# with #y# and solve for #y#.

#y = f(x) = (2x - 3)/(x+4)#

#x = (2y - 3)/(y+4)#

#xy + 4x = 2y - 3#

#4x + 3 = 2y - xy#

#4x + 3 = (2 - x)y#

#y_"inv" = f_("inv")(x) = (4x + 3)/(2-x)#

#f(x) = (2x - 3)/(x+4)#:
graph{y = (2x - 3)/(x+4) [-20, 20, -10, 10]}

#f_("inv")(x) = (4x + 3)/(2-x)#:
graph{y = (4x + 3)/(2-x) [-20, 20, -10, 10]}