PRACTICE PROBLEMS OF FINDING INVERSE FUNCTIONS

For each of the following functions :

Problem 1 :

a) f(x)  =  2x+5         Solution

b) f(x)  =  (3-2x)/4        Solution

c) f(x)  =  x+3        Solution

(i) Find f^-1(x)        Solution

(ii) sketch y  =  f(x), y  =  f^-1(x) and y  =  x on the same axes.        Solution

Problem 2 :

If f(x)  =  2x + 7, find :

a) f^-1(x)        b) f(f^-1(x))        c) f^-1(f(x))

Solution

Problem 3 :

If f(x)  =  (2x + 1)/(x + 3), find :

a) f^-1(x)     b) f(f^-1(x))     c) f^-1(f(x))

Solution

Problem 4 :

Find the inverse of the function f(x)  =  2x + 3.

Solution

Problem 5 :

Find the inverse of the function h(x)  =  log₁₀(x). 

Solution

(1) 

(a)  (i)  f^-1(x)  =  (x-5)/2

(ii)  

b)  (i)  f^-1(x)  =  -2x+(3/2)

(ii)

c) (i)  f^-1(x)  =  x-3

(ii) 

(2)  (a)  f^-1(x)  =  (x-7)/2

b)  f(f^-1(x))  =  x

c) f^-1(f(x))  =  x

(3)

(a)  f^-1(x)  =  (1-3x)/(x-2)

b)  f(f^-1(x))  =  x  ------(1)

c)  f^-1(f(x))  =  x  ------(2)

(4)  f^-1(x)  =  (x - 3) / 2

(5)  h^-1(x)  =  10^x

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