For which of the following functions does #f(x) = f^-1(x)#: A) #f(x) = (2x-1)/2#, B) #f(x) = 10-x#, C) #f(x) = x-4#, D) #f(x) = x+4#?

2 Answers
Dec 12, 2017

See below.

Explanation:

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

Now by inspection

#10-(10-x) = x = f(f(x))#

Dec 12, 2017

Answer B: #f^-1(x) = 10-x#

Explanation:

To find the inverse of a given function, simply swap #x# for #f^-1(x)# and #f(x)# for #x# and solve for #f^-1(x)#

Let's try each of the options in turn.

A.
#f(x) = (2x-1)/2#

#:. x = (2f^-1(x)-1)/2#

#2x = 2f^-1(x)-1#

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

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

#f^-1(x) != f(x)#

B.
#f(x) = 10-x#

#x = 10-f^-1(x)#

#f^-1(x) = 10-x#

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

C.
#f(x) = x-4#

#x= f^-1(x) -4#

#f^-1(x) = x+4#

#f^-1(x) != f(x)#

D.
#f(x) = x+4#

#x= f^-1(x) +4#

#f^-1(x) = x-4#

#f^-1(x) != f(x)#

Hence, answer B is the only one that satisfies #f^-1(x) = f(x)#