Tanya is given the graphs of the following functions. The functions Latex: f(x) f ( x ) and Latex: g(x) g ( x ) are linear, and the function Latex: s(x) s ( x ) is quadratic. f ( x ) = 3 x − 8 g ( x ) = − 2 x + 5 s ( x ) = 4 x 2 − 9 x + 2 Tanya is then asked to find the graph of Latex: (f\cdot g)(x) ( f ⋅ g ) ( x ) and the graph of Latex: (g\cdot s)(x)\textsf{.} For each combined function, she is given four options to choose from. What clues will help Tanya identify the correct graph of Latex: (f\cdot g)(x)\textsf{?} What clues will help Tanya identify the correct graph of Latex: (g\cdot s)(x)\textsf{?}

Respuesta :

The functions (f.g)(x) and (g.s)(x) are illustrations of composite function

The values of the composite functions are:

(fg)(x) = -6x^2 + 31x - 40 and (gs)(x) = -8x^3 + 38x^2 -49x+ 10

How to determine the equation of the composite function

The equation of the functions are given as:

f(x) = 3x - 8

g(x) = -2x + 5

s(x) = 4x^2 - 9x + 2

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The composite functions are calculated using:

(fg)(x) = f(x) * g(x)

So, we have:

(f g)(x) = (3x - 8) * (-2x + 5)

Evaluate the product

(fg)(x) = -6x^2 + 15x + 16x - 40

Evaluate the like terms

(fg)(x) = -6x^2 + 31x - 40

Also, we have:

(gs)(x) = g(x) * s(x)

So, we have:

(gs)(x) = (-2x + 5) * (4x^2 - 9x + 2)

Expand

(gs)(x) = -8x^3 + 18x^2 -4x + 20x^2 - 45x + 10

Collect like terms

(gs)(x) = -8x^3 + 18x^2 + 20x^2-4x - 45x + 10

Evaluate the like terms

(gs)(x) = -8x^3 + 38x^2 -49x+ 10

Hence, the values of the composite functions are:

(fg)(x) = -6x^2 + 31x - 40 and (gs)(x) = -8x^3 + 38x^2 -49x+ 10

Read more about composite functions at:

https://brainly.com/question/10687170