FINDING INVERSE OF A FUNCTION

Find the inverse of each function. Then graph the function and its inverse.

Problem 1 :

f(x) = x + 3

Solution :

f(x) = x + 3

In the above function f(x) to be replaced by ‘y’.

y = x + 3

Solve for x,

x = y - 3

Replace x by f^-1(x) and y by x

f^-1(x) = x - 3

Problem 2 :

f(x) = (x - 2)/ 5

Solution:

Given function,

f(x) = (x - 2)/ 5

In the above function f(x) to be replaced by ‘y’. 

y = (x - 2)/ 5

Solve for x,

5y = x - 2

x = 5y + 2

Replace x by f^-1(x) and y by x

f^-1(x) = 5x + 2

Problem 3 :

f(x) = x² - 4

Solution :

f(x) = x² - 4

In the above function f(x) to be replaced by ‘y’. 

y = x² - 4

x² = y + 4

x = ± √y + 4

Replace x by f^-1(x) and y by x

f^-1(x) = ± √x + 4

Problem 4 :

f(x) = -7x - 9

Solution :

f(x) = -7x - 9

In the above function f(x) to be replaced by ‘y’. 

y = -7x - 9

7x = -y - 9

x = (-y - 9)/7

Replace x by f^-1(x) and y by x

f^-1(x) = (-x - 9)/7