Given the functions f(x) = x^2 and g(x) = 3x-2, determine how the vertex of the composite function would differ between (fg)(x) and (gf)(x)

The vertex of

The vertex of

Step-by-step explanation:

Given : Functions   and  

To determine : How the vertex of the composite function would differ between (fg)(x) and (gf)(x)          

Solution : First we find the composite function

and  

1)

For   substitute x with  

Vertex form is

Comparing with  

a=9, vertex

Therefore, The vertex of   ........[1]

2)

For substitute x with  

To find the vertex of a quadratic function the vertex is

Comparing with

a=3 b=0,c=-2 substitute value,

Therefore, The vertex of ...........[2]

Hence, The vertex of the composite function differ between and by [1] and [2]

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step-by-step explanation:

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step-by-step explanation: