The functions f and g are defined on the set, R, of real numbers by \(f : x \to x^{2} - x - 6\) and \(g : x \to x - 1\). Find \(f \circ g(3)\).

The functions f and g are defined on the set, R, of real numbers by \(f : x \to x^{2} - x - 6\) and \(g : x \to x - 1\). Find \(f \circ g(3)\).

Answer Details

To find \(f \circ g(3)\), we first need to apply the function g to the input 3. Since \(g : x \to x - 1\), we have: \[g(3) = 3 - 1 = 2.\] Now we can use the output of g(3) as the input to the function f. Since \(f : x \to x^{2} - x - 6\), we have: \[f(g(3)) = f(2) = 2^{2} - 2 - 6 = -4.\] Therefore, the value of \(f \circ g(3)\) is -4