Question

Give an example of a function which represents all types of a function. Find the composite function (fog)(x) given that f = {(1,6), (4,7), (5,0)) and g = {(6,1), (7,4), (0,5)}

Answer 1

(fog)(x) = x

Explanation:

Composite function:

`(f \circ g)(x) = f(g(x))`

Composite of a function and its inverse.

The composition of a function and it's inverse is the straight line x. So

`(f \circ f^(-1))(x) = x`

f = {(1,6), (4,7), (5,0)) and g = {(6,1), (7,4), (0,5)}

We can see that the x-values in f are the y-values for g, and the y-values for f are the x-values for g, that is, f and g are inverse functions. Thus:

(fog)(x) = x