How do you find the inverse of #f(x)=2x-3# and graph both f and #f^-1#?

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Answer 1 · 2018-06-26T02:34:35

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

To make the function easier to work with, first replace #f(x)# with #y#:
#y = 2x-3#

To find the inverse of the relation, swap #x# and #y#:
#x = 2y - 3#

Solve for #y#:
#x+3=2y#

#y=(x+3)/2#

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

To graph the functions, first substitute some values of #x# into #f(x)#:

#f(0) = -3# gives the point #(0,-3)#
#f(1)=-1# gives the point #(1,-1)#
#f(2)=1# gives the point #(2,1)#

Graph these points and label the graph #f(x)#.

The points of #f^-1(x)# can be obtained by "reversing" the points of #f(x)#.

#(0,-3) => (-3,0)#
#(1,-1) => (-1,1)#
#(2,1) => (1,2)#

Graphing these points gives the graph of #f^-1(x)#.