Question

use the graph shown to evaluate the composition.

\\((f \circ g)(0) = \\)

Explanation:

Define the composition of functions

$$ (f \circ g)(0) = f(g(0)) $$

Evaluate the inner function g(0) from the graph

The parabola represents \(g(x)\) and has a \(y\)-intercept at \((0, 2)\):

$$ g(0) = 2 $$

Evaluate the outer function f(2) from the graph

The line represents \(f(x)\). At \(x = 2\), the line passes through the grid intersection at \(y = 1\):

$$ f(2) = 1 $$

Therefore:

$$ (f \circ g)(0) = f(2) = 1 $$

Answer:

Use the graph shown to evaluate the composition.

\( (f \circ g)(0) = \) <blank>1</blank>