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

1 Answer
Jun 26, 2018

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

Explanation:

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).