What is the inverse of f(x) = -1/5x -1 ?

2 Answers
Sep 29, 2015

#f(y) = (y-1)/(5y)#

Explanation:

Replace #f(x)# by #y#

#y = -1/(5x-1)#

Invert both sides

#1/y= -(5x-1)#

Isolate #x#

#1-1/y = 5x#
#1/5-1/(5y) = x#

Take the least common divisor to sum the fractions

#(y-1)/(5y) = x#

Replace #x# for #f(y)#

#f(y) = (y-1)/(5y)#

Or, in #f^(-1)(x)# notation, replace #f(y)# for #f^(-1)(x)# and #y# for #x#

#f^(-1)(x) = (x-1)/(5x)#

I personally prefer the former way though.

Sep 29, 2015

#g(x) = -5x-5#
is the inverse of #f(x)=-1/5x-1#

Explanation:

If #g(x)# is the inverse of #f(x)#
then #f(g(x)) = x#

Replacing #x# with #g(x)# in the original equation and
recognizing that #f(g(x)) = x#
we have
#color(white)("XXX")f(g(x)) = -1/5g(x)-1=x#

#rarrcolor(white)("XXXXXXXX")-1/5g(x) =x+1#

#rarrcolor(white)("XXXXXXXX")g(x) = (-5)(x+1) = -5x-5#