Question

1. A function f : Z → Z is defined by f(n) = 3n − 9....

1. A function f : Z → Z is defined by f(n) = 3n − 9.

(a) Determine f(C), where C is the set of odd integers.

(b) Determine f^−1 (D), where D = {6k : k ∈ Z}.

2. Two functions f : Z → Z and g : Z → Z are defined by f(n) = 2n^ 2+1 and g(n) = 1 − 2n. Find a formula for the function f ◦ g.

3. A function f : R − { 1/2 } → R − {0} is defined by

f(x) = 3/(2x − 1) .

Prove that f is bijective.

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