What is the inverse function of #f(x)=(2x+5)/(5x-3)#?

1 Answer
Sep 10, 2015

#f^(-1)(x) = (3x+5)/(5x-2)#

Explanation:

For ease of manipulation replace #f(x)# with #y#

#y = (2x+5)/(5x-3)#

#rarrcolor(white)("XX")5xy-3y = 2x+5#

#rarrcolor(white)("XX")5xy-2x=3y+5#

#rarrcolor(white)("XX")x(5y-2) = 3y+5#

provided #5y-2!=0#
#rarrcolor(white)("XX")x=(3y+5)/(5y-2)#

For the inverse function (which I will write as #f^(-1)(x)#) exchange the #x# and #y# variables, then replace #y# with #f^(-1)(x)#

#rarrcolor(white)("XX")f^(-1)(x) = (3x+5)/(5x-2)#