Questions: (fg)(x) = (√(3-x))(√(x^2-1))

Solution Steps

To solve the given function \((f g)(x) = (\sqrt{3-x})(\sqrt{x^2-1})\), we need to:

1. Define the function in Python.
2. Evaluate the function for a given value of \(x\).

Given the function \((f g)(x) = (\sqrt{3-x})(\sqrt{x^2-1})\), we need to evaluate it for a specific value of \(x\).

We substitute \(x = 2\) into the function: \[ (f g)(2) = (\sqrt{3-2})(\sqrt{2^2-1}) \]

Simplify the terms inside the square roots: \[ \sqrt{3-2} = \sqrt{1} = 1 \] \[ \sqrt{2^2-1} = \sqrt{4-1} = \sqrt{3} \]

Multiply the simplified terms: \[ (f g)(2) = 1 \cdot \sqrt{3} = \sqrt{3} \]

The numerical value of \(\sqrt{3}\) is approximately \(1.7321\).

Final Answer