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Use the graph shown to evaluate the composition. (fxg)(0)

Use the graph shown to evaluate the composition. (fxg)(0)-example-1
User Nyeema
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1 Answer

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Answer:

(f∘g)(0) = 3

Explanation:

You want the composition (f∘g)(0), given f(x) = 2x-1 and g(x) = -x²+2.

Graph

The line x=0 (y-axis) intersects the curve g(x) at g(0) = 2.

The line x=2 intersects the curve f(x) at f(2) = 3.

The value of the composition is ...

(f∘g)(0) = f(g(0)) = f(2) = 3

The composition value is 3.

__

Additional comment

Using the equations, we have ...

(f∘g)(x) = 2(-x² +2) -1 = -2x² +4 -1 = -2x² +3

(f∘g)(0) = -2·0² +3 = 3

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User Josiah Hudson
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