Answered

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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)}

Sagot :

Answer:

(fog)(x) = x

Step-by-step explanation:

Composite function:

[tex](f \circ g)(x) = f(g(x))[/tex]

Composite of a function and its inverse.

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

[tex](f \circ f^{-1})(x) = x[/tex]

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

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