Question

2. Given each of the following functions that maps X-1, 23) to Y= {A, B, C)(20 points, 2 parts- 10 points each) b. g(1) C, g(2) -B, g3) A Determine whether the function has an inverse. If it has an inverse, provide it. If it does not, explain why not

Answer 1

Not all functions have a inverse. When there exists one to one relationship between i and j such that F(i) = j, where f is a function that transforms input i to one and only output j.

A function G(j) = i, which means that by applying function with input as j,output is i. Then it can be said that function F has function G as its inverse function.

(a) f(1) = A and f(3) = A, here 2 inputs {1,3} give A as result. Hence there is Many to One relationship between input and output. Hence function f(x) does not have a inverse.

(b) g(1) = C, g(2) = B , g(3) = A, here all inputs {1,2,3} have one and only one output {C,B,A}, in same sequence, hence showing one to one relationship between input set and output set. Hence the function g has a inverse.

Below is the inverse function -

Let H be a function where -

h(A) = 3, h(B) = 2 and h(C) = 1, then h can be called as inverse function of g. (g^-1 = h)