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2. Let f(x) = x2 +1 and g(x) = {x+1, x> =3; x-1, x<3 so both f and g map R into
Find the formula for
a. (f+g)(x)
b. (f .g)(x)
c. (f o g)(x)
d. (g o f)(x)

3. Let A = {a,b,c,d} and B = {1,2,3} and let f : A &#61664; B be a function . Let g : Z &#61664; 2Z, where 2Z = {0,+-2,+-4,+-6 ...}
a. Could f be one to one? Must f be one to one? Explain
b. Could f be onto? Must f be onto? Explain
c. Could g be one to one? Must g be one to one? Explain
d. Could g be onto? Must g be onto? Explain

4. Let &#8801; be the relation on Z given by n &#8801; m mod 5 iff 5|(n-m). Show that equivalence mod 5 is an equivalence relation on Z.

5. Let f : A &#61664; B, g : B &#61664; C so that g o f : A &#61664; C is a function from A to C and suppose that g o f is one to one.
a. Show that f is one to one
b. Show that if in addition f is onto, g is one to one


Solution Summary

This solution is comprised of a detailed explanation to find the formula.