Define the following functions f g and h f 0 130 13 The outp

Define the following functions f, g, and h:

f: {0, 1}3{0, 1}3. The output of f is obtained by taking the input string and replacing the first bit by 1, regardless of whether the first bit is a 0 or 1. For example, f(001) = 101 and f(110) = 110.

g: {0, 1}3{0, 1}3. The output of g is obtained by taking the input string and reversing the bits. For example, g(011) = 110.

h: {0, 1}3{0, 1}3. The output of h is obtained by taking the input string x, and replacing the last bit with a copy of the first bit. For example, h(011) = 010.

A. What is g f(010)?

B. What is g h(010)?

C. What is the range of h f?

D. What is the range of g f?

Solution

a)

gof(010)=g(f(010)

=g(110)

=011

b)

goh(010)=g(h(010)

=g(010)

=010

c) range of hof is(0,1)3

d) range of gof is (0,1)3