Final answer:
To calculate g(f(2)), we first determine f(2), which equals 3, and then apply g(x) to 3, resulting in a final value of 10 for g(f(2)).
Step-by-step explanation:
To find g(f(2)), we first need to compute f(2). The function f(x) is given by f(x) = √(x²+5). Plugging in 2 for x, we get:
f(2) = √(2²+5) = √(4+5) = √9 = 3.
Next, we use this value as the input for the function g(x), where g(x) = x² + x - 2. Hence:
g(f(2)) = g(3) = 3² + 3 - 2 = 9 + 3 - 2 = 10.
Therefore, g(f(2)) equals 10.