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#?

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Answer 1 · 2017-12-12T01:06:03

See below.

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

Now by inspection

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

Answer 2 · 2017-12-12T01:21:26

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

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)#